Equation 677 Database

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Magma 21df2a4a111c…

magma 21df2a4a111c
Size
720
Isomorphism class hash
21df2a4a111c4685f430f1e9541b07d634af1bcd867f41b3ee98c4fef756e785
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 719) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 23:35:19
Display reorder
19,20,21,22,23,24,25,26,27,13,14,15,16,17,18,719,520,529,562,563,521,530,564,522,531,565,508,532,566,509,533,567,510,534,553,511,535,554,512,536,555,513,537,556,514,523,557,515,524,558,516,525,559,517,526,518,560,527,519,561,528,545,552,538,539,540,541,542,543,544,547,548,549,550,551,546,677,676,678,675,316,272,307,308,317,273,309,318,274,310,319,275,311,320,276,312,321,277,298,322,278,299,323,279,300,324,280,301,325,281,302,326,282,303,327,268,304,313,269,314,305,270,315,306,271,289,296,297,283,284,285,286,287,288,291,292,293,294,295,290,703,705,704,706,599,624,657,643,600,625,644,601,626,645,602,627,646,603,613,647,604,614,648,605,615,649,606,616,650,607,617,651,608,618,652,609,619,653,610,620,654,611,621,612,655,622,598,656,623,640,632,633,634,635,636,637,638,639,642,628,629,630,631,641,683,685,684,686,335,345,380,381,336,346,382,337,347,383,338,348,384,339,349,385,340,350,386,341,351,387,342,352,373,328,353,374,329,354,375,330,355,376,331,356,377,332,357,333,378,343,334,379,344,361,368,369,370,371,372,358,359,360,363,364,365,366,367,362,691,694,692,693,137,95,128,129,138,96,130,139,97,131,140,98,132,141,99,118,142,100,119,143,101,120,144,102,121,145,88,122,146,89,123,147,90,124,133,91,125,134,92,135,126,93,136,127,94,111,103,104,105,106,107,108,109,110,113,114,115,116,117,112,679,682,680,681,671,672,674,673,568,582,659,569,12,660,570,1,661,571,0,662,572,2,663,573,3,664,574,4,665,575,5,666,576,6,667,577,7,668,578,8,669,579,9,580,670,10,581,658,11,597,589,590,591,592,593,594,595,596,584,585,586,587,588,583,710,708,709,707,87,30,63,64,73,31,65,74,32,66,75,33,67,76,34,68,77,35,69,78,36,70,79,37,71,80,38,72,81,39,58,82,40,59,83,41,60,84,42,85,61,28,86,62,29,46,53,54,55,56,57,43,44,45,48,49,50,51,52,47,718,716,717,715,169,179,159,160,170,180,161,171,181,162,172,182,148,173,183,149,174,184,150,175,185,151,176,186,152,177,187,153,163,188,154,164,189,155,165,190,156,166,191,167,157,192,168,158,178,195,202,203,204,205,206,207,193,194,197,198,199,200,201,196,714,712,713,711,449,473,507,493,450,474,494,451,475,495,452,476,496,453,477,497,454,463,498,455,464,499,456,465,500,457,466,501,458,467,502,459,468,503,460,469,504,461,470,462,505,471,448,506,472,490,482,483,484,485,486,487,488,489,492,478,479,480,481,491,687,689,688,690,211,236,256,257,212,237,258,213,223,259,214,224,260,215,225,261,216,226,262,217,227,263,218,228,264,219,229,265,220,230,266,221,231,267,222,232,253,208,233,209,254,234,210,255,235,238,245,246,247,248,249,250,251,252,240,241,242,243,244,239,698,697,696,695,435,391,425,426,436,392,427,437,393,428,438,394,429,439,395,430,440,396,431,441,397,432,442,398,418,443,399,419,444,400,420,445,401,421,446,402,422,447,388,433,423,389,434,424,390,408,415,416,417,403,404,405,406,407,410,411,412,413,414,409,701,700,702,699 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 720 = 16 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#9ec34e5d7233e8953a2fa801c206b195473c59d0c7836b1f0f582edb83284699, M = {0, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 44, 48, 54, 58, 77} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-07 23:35:20 · history