Equation 677 Database

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Magma 8bdefa528f19…

magma 8bdefa528f19
Size
705
Isomorphism class hash
8bdefa528f192d269b61275a49e6e05681180eb4cff0e15143259162be9f8491
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 18:18:54
Display reorder
660,386,146,518,446,202,144,203,384,516,444,145,201,385,517,445,389,198,149,521,449,387,199,147,519,447,388,200,148,520,448,193,152,524,392,452,194,150,522,390,450,192,151,523,391,451,196,155,527,395,455,393,197,153,525,453,195,154,526,394,454,661,664,666,667,275,324,252,47,482,325,480,273,253,45,326,481,274,254,46,271,485,327,255,43,272,483,328,256,44,270,484,329,257,42,488,330,258,266,38,486,331,259,264,36,487,332,260,265,37,491,333,261,269,41,267,489,334,262,39,490,335,263,268,40,688,690,692,686,374,163,554,572,63,164,64,372,552,570,162,65,373,553,571,377,62,166,557,575,375,60,167,555,573,376,61,165,556,574,69,161,560,380,578,70,159,558,378,576,71,160,559,379,577,68,157,563,383,581,381,66,158,561,579,67,156,562,382,580,671,663,670,669,344,49,280,350,422,50,420,342,281,348,48,421,343,279,349,347,425,52,276,353,345,423,53,277,351,346,424,51,278,352,428,55,286,339,356,426,56,287,340,354,427,54,285,341,355,431,58,282,338,359,336,429,59,283,357,430,57,284,337,358,677,676,674,673,290,11,362,530,109,9,110,288,360,528,10,108,289,361,529,293,112,7,365,533,291,113,8,363,531,292,111,6,364,532,115,2,368,296,536,116,1,366,294,534,114,0,367,295,535,118,5,371,299,539,297,119,3,369,537,117,4,370,298,538,672,665,668,662,506,205,410,434,406,206,407,504,408,432,204,405,505,409,433,509,402,208,413,437,507,403,209,411,435,508,404,207,412,436,397,211,416,512,440,398,212,414,510,438,396,210,415,511,439,400,214,419,515,443,513,401,215,417,441,399,213,418,514,442,693,698,695,694,16,78,18,584,568,79,569,17,19,582,80,567,15,20,583,12,564,81,21,587,13,565,82,22,585,14,566,83,23,586,644,76,646,645,647,639,77,637,636,638,640,75,642,641,643,656,72,658,657,659,648,649,73,650,651,653,74,654,652,655,702,701,704,703,126,105,494,590,303,106,304,127,492,588,107,305,128,493,589,129,302,104,497,593,130,300,102,495,591,131,301,103,496,592,309,96,500,124,596,310,97,498,125,594,311,98,499,123,595,308,99,503,120,599,121,306,100,501,597,307,101,502,122,598,696,700,699,697,85,132,186,248,542,133,540,86,187,246,134,541,84,188,247,88,545,135,189,251,89,543,136,190,249,87,544,137,191,250,548,138,184,91,243,546,139,185,92,244,547,140,183,90,245,551,141,180,94,242,95,549,142,181,240,550,143,182,93,241,679,680,682,684,626,321,32,602,458,322,456,624,30,600,323,457,625,31,601,629,461,320,35,605,627,459,318,33,603,628,460,319,34,604,464,312,27,632,608,462,313,28,630,606,463,314,29,631,607,467,315,26,635,611,633,465,316,24,609,466,317,25,634,610,678,683,681,675,233,168,222,470,614,169,612,231,223,468,170,613,232,224,469,229,617,171,225,473,230,615,172,226,471,228,616,173,227,472,620,174,220,239,476,618,175,221,237,474,619,176,219,238,475,623,177,216,235,479,236,621,178,217,477,622,179,218,234,478,691,689,687,685 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#789271f8e1620c5f8875a1b32dfd6da1b71c443ca3fc9082ace33bb0fcd8a22c, 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 18:18:57 · history