Equation 677 Database

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Magma 998b023837aa…

magma 998b023837aa
Size
705
Isomorphism class hash
998b023837aa3c270998513b75908b39d3dd5ca237ca5fcd21043b53b9aec27a
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 17:18:59
Display reorder
660,172,32,426,573,549,173,30,427,574,550,171,31,428,575,551,35,175,425,572,548,33,176,423,570,546,34,174,424,571,547,417,170,27,564,540,418,168,28,565,541,419,169,29,566,542,166,420,26,567,543,167,421,24,568,544,165,422,25,569,545,687,685,682,678,513,120,283,348,338,514,121,284,349,336,515,122,282,350,337,123,512,279,347,334,124,510,280,345,335,125,511,281,346,333,274,504,118,339,329,275,505,119,340,327,273,506,117,341,328,507,277,114,342,332,508,278,115,343,330,509,276,116,344,331,662,661,670,666,411,186,525,477,20,412,187,526,478,18,413,188,527,479,19,185,410,524,476,23,183,408,522,474,21,184,409,523,475,22,516,402,177,468,15,517,403,178,469,16,518,404,179,470,17,405,519,180,471,14,406,520,181,472,12,407,521,182,473,13,681,673,676,683,642,68,636,638,641,650,66,644,646,649,658,67,652,654,657,71,634,629,630,633,69,618,613,614,617,70,626,621,622,625,73,414,63,126,389,74,415,64,127,387,72,416,65,128,388,591,588,62,593,592,602,597,60,598,601,610,605,61,606,609,704,697,699,703,43,208,306,501,48,44,209,307,502,49,42,207,308,503,50,211,46,305,500,51,212,47,303,498,52,210,45,304,499,53,297,41,206,492,54,298,39,204,493,55,299,40,205,494,56,37,300,202,495,57,38,301,203,496,58,36,302,201,497,59,693,690,692,689,109,143,95,537,489,110,141,93,538,490,108,142,94,539,491,146,105,98,536,488,144,106,96,534,486,145,107,97,535,487,90,100,149,528,480,91,101,147,529,481,92,99,148,530,482,103,89,152,531,483,104,87,150,532,484,102,88,151,533,485,671,669,665,667,239,309,225,215,250,237,310,226,213,251,238,311,227,214,249,312,242,228,218,253,313,240,229,216,254,314,241,230,217,252,231,245,315,221,256,232,243,316,219,257,233,244,317,220,255,248,234,318,224,259,246,235,319,222,260,247,236,320,223,258,694,695,696,691,399,135,561,438,585,400,136,562,439,586,401,137,563,440,587,138,398,560,437,584,139,396,558,435,582,140,397,559,436,583,552,390,133,429,576,553,391,134,430,577,554,392,132,431,578,393,555,129,432,579,394,556,130,433,580,395,557,131,434,581,679,688,675,686,639,272,643,637,640,647,270,651,645,648,655,271,659,653,656,268,631,635,628,632,269,615,619,612,616,267,623,627,620,624,455,321,263,111,325,453,322,261,112,326,454,323,262,113,324,594,595,266,589,590,599,603,264,596,600,607,611,265,604,608,702,700,698,701,384,294,367,465,195,385,295,368,466,196,386,296,366,467,197,293,383,363,464,198,291,381,364,462,199,292,382,365,463,200,373,375,285,456,193,374,376,286,457,194,372,377,287,458,192,378,369,288,459,189,379,370,289,460,190,380,371,290,461,191,668,672,663,664,450,83,0,162,360,451,81,2,163,361,452,82,1,164,362,86,449,4,161,359,84,447,5,159,357,85,448,3,160,358,7,441,78,153,351,8,442,79,154,352,6,443,80,155,353,444,10,77,156,354,445,11,75,157,355,446,9,76,158,356,677,674,680,684 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#4dbd6b0006d3996c22611f6a9a74b6d8666415e8467cb95ff3380ed5b17e9234, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 17:19:00 · history