Equation 677 Database

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Magma 6d5f71070e99…

magma 6d5f71070e99
Size
707
Isomorphism class hash
6d5f71070e9968a359257552dbf9f54e2ddcf88d70a52133be81f0cd1146542c
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 13:20:00
Display reorder
497,499,498,500,501,525,643,121,123,122,125,120,124,198,203,199,200,201,202,215,214,210,211,212,213,97,96,98,99,100,101,109,108,110,111,112,113,187,186,188,189,190,191,174,179,175,176,177,178,131,130,126,127,128,129,140,139,141,142,143,138,168,173,169,170,171,172,161,160,156,157,158,159,147,146,148,149,144,145,490,489,488,487,485,486,558,560,559,561,562,563,557,556,555,554,552,553,450,449,451,454,452,453,373,372,374,375,376,377,475,474,473,476,477,478,361,362,360,365,363,364,460,459,458,455,456,457,610,606,611,609,607,618,634,635,681,697,653,679,680,651,704,695,694,706,696,699,17,13,12,15,16,14,24,29,25,26,27,28,32,31,33,34,35,30,284,283,285,286,287,282,288,293,289,290,291,292,272,271,273,274,275,270,58,57,59,54,55,56,250,249,251,246,247,248,333,332,334,335,331,330,63,62,64,65,60,61,260,259,261,262,263,258,326,325,327,324,328,329,531,533,532,528,529,530,384,386,385,387,526,388,571,570,572,568,569,567,392,394,393,390,391,389,412,411,410,408,409,407,510,509,508,511,512,513,536,535,534,538,539,537,522,521,520,523,524,527,612,615,608,617,616,613,636,632,688,687,669,675,685,648,686,667,683,701,674,673,167,163,162,165,166,164,182,181,183,184,185,180,86,85,87,88,89,84,5,4,1,0,2,3,155,154,150,151,152,153,134,133,135,136,137,132,107,106,102,103,104,105,115,114,116,117,118,119,204,209,205,206,207,208,95,94,90,91,92,93,220,219,221,216,217,218,197,196,192,193,194,195,472,471,470,469,467,468,483,482,484,480,481,479,603,605,604,601,600,602,400,399,398,395,396,397,599,598,597,594,596,595,462,461,463,466,464,465,546,548,547,551,549,550,445,444,443,446,447,448,630,631,629,622,627,628,621,637,662,698,676,689,661,649,682,690,691,703,658,663,45,47,46,43,44,42,252,257,253,254,255,256,50,49,51,52,53,48,305,304,300,301,302,303,294,299,295,296,297,298,345,344,346,343,342,347,323,322,318,319,320,321,269,268,264,265,266,267,278,277,279,280,281,276,38,37,39,40,41,36,20,19,21,22,23,18,336,337,338,339,340,341,540,542,541,543,544,545,578,577,576,581,579,580,378,380,379,381,382,383,588,589,590,593,591,592,515,514,516,517,518,519,418,417,416,413,414,415,503,502,504,505,506,507,585,584,586,582,583,587,626,624,620,625,614,623,619,633,672,705,655,700,666,650,692,684,670,702,677,668,356,358,357,355,354,359,77,76,72,73,74,75,79,78,80,81,82,83,311,310,306,307,308,309,349,350,348,351,352,353,242,241,243,244,245,240,231,230,232,233,228,229,224,223,225,226,227,222,235,234,236,237,238,239,11,10,6,7,8,9,68,67,69,70,71,66,313,312,314,315,316,317,574,573,575,566,564,565,366,368,367,369,370,371,401,403,402,404,405,406,421,420,419,422,423,424,496,495,494,492,493,491,431,433,432,435,436,434,430,429,428,426,427,425,442,441,440,437,438,439,646,639,640,641,644,645,642,638,664,693,654,665,678,647,657,660,659,671,652,656 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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, 5, B) with E = magma#7c5787f3763007370795fcf378d2af7959e084037efbb89592fd99450acc2142, M = {96, 97, 98, 99, 100, 101, 129} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 140): MacNeish's product over GF(4) x GF(5) x GF(7); GF(4) = F_2[x]/(x^2 + 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: 101.

last edited by qawbecrdtey at 2026-10-06 13:20:06 · history