Equation 677 Database

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Magma f455f2828d01…

magma f455f2828d01
Size
705
Isomorphism class hash
f455f2828d01069ba8b9e746f1e24bdb2e010aebd66693b62a1de6d66f3cfa69
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 20:44:43
Display reorder
660,379,219,499,287,547,285,220,380,500,548,286,221,378,498,546,218,283,382,502,550,216,284,383,503,551,217,282,381,501,549,278,377,497,225,545,276,375,495,226,543,277,376,496,227,544,373,281,493,224,541,374,279,494,222,542,372,280,492,223,540,671,661,670,662,4,535,367,176,86,174,536,5,368,87,175,534,3,366,88,538,179,1,370,89,539,177,0,371,90,537,178,2,369,91,171,10,365,533,84,172,11,363,531,85,173,9,364,532,83,6,170,361,529,80,7,168,362,530,81,8,169,360,528,82,685,690,686,687,247,487,335,94,391,92,488,248,333,392,93,486,246,334,390,490,97,250,331,394,491,95,251,332,395,489,96,249,330,393,100,245,326,485,389,98,243,324,483,387,99,244,325,484,388,241,103,329,481,385,242,101,327,482,386,240,102,328,480,384,663,666,672,669,439,114,134,191,427,189,112,440,135,428,190,113,438,133,426,117,187,442,130,430,115,188,443,131,431,116,186,441,132,429,182,437,125,120,425,180,435,126,118,423,181,436,124,119,424,433,185,128,123,421,434,183,129,121,422,432,184,127,122,420,675,681,673,680,463,403,415,73,475,71,404,464,416,476,72,402,462,414,474,406,69,466,418,478,407,70,467,419,479,405,68,465,417,477,79,461,413,401,473,77,459,411,399,471,78,460,412,400,472,457,75,409,397,469,458,76,410,398,470,456,74,408,396,468,668,667,665,664,587,289,303,231,323,232,290,588,304,321,233,288,586,305,322,292,230,590,302,319,293,228,591,300,320,291,229,589,301,318,237,585,309,295,314,238,583,310,296,312,239,584,311,294,313,581,236,308,298,317,582,234,306,299,315,580,235,307,297,316,693,697,694,695,579,105,48,60,635,61,646,647,645,644,59,104,578,49,634,653,56,652,655,654,657,57,656,659,658,649,58,648,651,650,66,577,54,111,629,67,575,55,109,630,65,576,53,110,628,573,62,50,107,632,574,63,51,108,633,572,64,52,106,631,702,703,704,701,148,611,567,142,552,143,612,636,568,637,144,610,149,566,559,614,145,641,570,640,615,146,643,571,642,613,147,639,569,638,140,154,565,609,558,141,155,563,607,556,139,153,564,608,557,150,136,561,605,554,151,137,562,606,555,152,138,560,604,553,700,699,696,698,33,599,270,206,451,204,600,34,271,452,205,598,35,272,450,602,209,32,273,454,603,207,30,274,455,601,208,31,275,453,212,24,268,597,449,210,25,269,595,447,211,26,267,596,448,27,215,264,593,445,28,213,265,594,446,29,214,266,592,444,676,679,684,682,523,511,167,359,623,357,512,524,165,624,358,510,522,166,622,514,355,526,163,626,515,356,527,164,627,513,354,525,162,625,350,521,158,509,621,348,519,156,507,619,349,520,157,508,620,517,353,161,505,617,518,351,159,506,618,516,352,160,504,616,683,678,674,677,200,44,344,252,22,253,42,198,342,23,254,43,199,343,21,47,255,203,347,18,45,256,201,345,19,46,257,202,346,20,258,195,339,39,13,259,196,340,40,14,260,197,341,41,12,194,261,338,38,16,192,262,336,36,17,193,263,337,37,15,688,689,692,691 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 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#d283ee665ba0250146cee526d5335dad060ba0eb857bd84eda99570515d555dc, M = {60} 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 2026-10-03 20:44:44 · history