Equation 677 Database

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Magma a0d171afdbb6…

magma a0d171afdbb6
Size
705
Isomorphism class hash
a0d171afdbb6b4626f964f8184beb1c3900f62a6ff50c3cbd0a902dc21cba38d
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 21:08:38
Display reorder
660,157,534,253,354,455,155,532,251,355,453,156,533,252,356,454,530,153,249,353,451,531,154,250,351,452,529,152,248,352,450,148,244,540,345,461,146,242,538,346,459,147,243,539,347,460,247,151,536,348,457,245,149,537,349,458,246,150,535,350,456,678,687,677,681,62,82,400,100,113,63,83,398,101,114,61,84,399,102,112,81,65,396,99,109,79,66,397,97,110,80,64,395,98,111,60,406,88,91,104,58,404,89,92,105,59,405,90,93,103,402,56,87,94,107,403,57,85,95,108,401,55,86,96,106,672,666,662,670,169,577,388,362,498,167,575,386,360,496,168,576,387,361,497,573,165,384,358,494,574,166,385,359,495,572,164,383,357,493,160,394,583,368,504,158,392,581,366,502,159,393,582,367,503,390,163,579,364,500,391,161,580,365,501,389,162,578,363,499,680,673,675,685,186,448,378,0,371,187,446,376,2,372,185,447,377,3,370,444,182,381,4,374,445,183,379,5,375,443,184,380,6,373,192,655,657,653,654,193,639,641,637,638,191,647,649,645,646,620,188,622,624,625,631,189,633,629,630,382,190,449,1,369,704,698,703,700,124,522,412,589,259,125,520,410,587,257,126,521,411,588,258,518,123,408,585,255,519,121,409,586,256,517,122,407,584,254,115,418,528,595,265,116,416,526,593,263,117,417,527,594,264,414,118,524,591,261,415,119,525,592,262,413,120,523,590,260,689,693,690,691,28,486,170,436,298,29,484,171,434,296,30,485,172,435,297,482,27,173,432,301,483,25,174,433,299,481,26,175,431,300,19,176,492,442,293,20,177,490,440,294,21,178,491,441,295,179,22,488,438,292,180,23,489,439,290,181,24,487,437,291,661,664,669,665,137,326,321,269,42,138,327,322,270,40,136,328,320,271,41,329,133,324,268,38,330,134,325,266,39,331,135,323,267,37,128,319,332,275,33,129,317,333,276,31,127,318,334,277,32,315,131,335,274,36,316,132,336,272,34,314,130,337,273,35,695,694,696,692,18,474,288,613,546,16,472,289,611,544,17,473,287,612,545,470,14,284,609,542,471,15,285,610,543,469,13,286,608,541,9,279,480,619,552,7,280,478,617,550,8,278,479,618,551,282,12,476,615,548,283,10,477,616,549,281,11,475,614,547,682,688,674,679,76,567,342,467,141,77,565,343,465,142,78,566,344,466,140,570,75,341,463,144,568,73,339,464,145,569,74,340,462,143,67,652,659,658,656,68,636,643,642,640,69,644,651,650,648,626,70,627,623,621,628,71,635,634,632,338,72,571,468,139,699,701,697,702,52,558,601,424,510,53,556,599,422,508,54,557,600,423,509,554,51,597,420,506,555,49,598,421,507,553,50,596,419,505,43,607,564,430,516,44,605,562,428,514,45,606,563,429,515,603,46,560,426,512,604,47,561,427,513,602,48,559,425,511,667,663,671,668,310,200,230,215,229,308,201,231,216,227,309,202,232,217,228,203,313,233,214,225,204,311,234,212,226,205,312,235,213,224,305,236,198,206,220,306,237,199,207,218,307,238,197,208,219,239,304,194,209,223,240,302,195,210,221,241,303,196,211,222,686,684,683,676 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#d958d834958932013e293186c3edbca2299f39c5df5a243bf65f8d4f2fad3f22, 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 21:08:39 · history