Equation 677 Database

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Magma ac61758ed69a…

magma ac61758ed69a
Size
705
Isomorphism class hash
ac61758ed69af9ab4b05395fbb610b28baa1754cb939cc3c4d12a6eac513769b
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 18:17:12
Display reorder
660,474,342,426,450,235,475,343,427,451,233,473,341,425,449,234,338,470,422,446,231,471,339,423,447,232,340,472,424,448,230,417,465,333,441,226,418,466,334,442,224,416,464,332,440,225,468,420,336,444,229,469,421,337,445,227,467,419,335,443,228,663,671,661,666,20,65,498,136,383,18,63,499,137,384,19,64,497,135,385,61,23,494,139,382,21,62,495,140,380,60,22,496,138,381,489,15,71,134,389,490,16,69,132,390,488,17,70,133,391,14,492,67,130,388,12,493,68,131,386,13,491,66,129,387,690,685,686,687,250,306,641,273,261,248,307,642,274,262,249,305,640,272,260,302,253,637,276,264,251,303,638,277,265,304,252,639,275,263,632,256,297,279,267,633,254,298,280,268,631,255,296,278,266,259,635,300,282,270,257,636,301,283,271,258,634,299,281,269,664,662,672,668,146,28,7,414,398,144,29,8,415,399,145,27,10,413,400,24,142,5,410,401,143,25,0,411,402,26,141,2,412,403,3,152,34,405,396,4,150,35,406,397,1,151,33,404,395,148,9,30,408,392,149,11,31,409,393,147,6,32,407,394,674,682,677,680,593,153,617,569,462,594,154,618,570,463,592,155,616,568,461,156,589,613,565,458,590,157,614,566,459,158,591,615,567,460,608,584,159,560,453,609,585,160,561,454,607,583,161,559,452,587,611,162,563,456,588,612,163,564,457,586,610,164,562,455,667,665,670,669,238,344,557,288,533,236,345,558,289,534,237,346,556,287,532,347,241,553,284,529,239,348,554,285,530,349,240,555,286,531,548,244,350,294,524,549,242,351,295,525,547,243,352,293,523,247,551,353,290,527,245,552,354,291,528,246,550,355,292,526,693,695,697,694,653,128,95,106,522,659,126,658,657,656,652,127,96,107,521,124,649,98,108,518,650,125,99,109,519,123,651,97,110,520,101,644,119,111,513,102,645,117,112,514,100,643,118,113,512,647,104,122,114,516,648,105,120,115,517,646,103,121,116,515,703,702,701,704,178,359,72,165,545,176,360,654,655,546,177,361,73,166,544,358,181,74,168,541,179,356,75,169,542,357,180,76,167,543,77,184,365,171,536,78,182,366,172,537,79,183,367,170,535,187,80,364,174,539,185,81,362,175,540,186,82,363,173,538,700,696,699,698,438,57,320,223,206,439,58,321,221,207,437,59,322,222,208,56,434,323,219,209,435,54,324,220,210,55,436,325,218,211,326,429,48,214,204,327,430,49,212,205,328,428,50,213,203,432,329,51,217,200,433,330,52,215,201,431,331,53,216,202,673,681,683,675,486,374,38,629,510,487,375,36,630,511,485,376,37,628,509,377,482,41,625,506,483,378,39,626,507,379,484,40,627,508,44,477,372,620,501,42,478,373,621,502,43,476,371,619,500,480,47,368,623,504,481,45,369,624,505,479,46,370,622,503,684,678,679,676,316,87,195,605,581,314,88,196,606,582,315,86,194,604,580,83,319,198,601,577,317,84,199,602,578,85,318,197,603,579,193,311,93,596,572,191,312,94,597,573,192,313,92,595,571,310,189,89,599,575,308,190,90,600,576,309,188,91,598,574,688,692,689,691 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#73fd82887325b6d09523ca7385118fdff4d39fe9410b39daf9f2816ebeaae0b3, 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 18:17:13 · history