Equation 677 Database

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Magma 7924aaa07602…

magma 7924aaa07602
Size
707
Isomorphism class hash
7924aaa07602731d85a146dc3c136ee4eaf5169c91942312001798a4b9ccf192
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 18:48:01
Display reorder
563,562,561,558,559,560,637,62,64,65,60,61,63,236,234,237,238,239,235,259,258,260,261,262,263,318,319,320,321,322,323,317,316,312,313,314,315,193,192,194,195,196,197,231,230,232,233,229,228,86,85,87,88,89,84,79,78,80,81,82,83,329,328,326,327,325,324,70,69,71,66,67,68,403,402,404,405,406,407,418,417,419,416,414,415,534,536,535,539,537,538,520,519,521,518,516,517,354,356,355,358,359,357,351,353,352,350,348,349,507,509,508,506,504,505,372,374,373,377,375,376,367,366,368,369,370,371,610,608,616,606,611,609,621,623,622,683,671,689,687,699,705,697,703,688,704,706,135,137,132,133,134,136,219,218,220,221,216,217,182,181,183,184,185,180,120,125,121,122,123,124,106,105,107,102,103,104,148,147,149,144,145,146,23,22,18,19,20,21,16,15,17,12,13,14,97,96,98,99,100,101,95,94,90,91,92,93,47,46,42,43,44,45,342,344,343,347,345,346,481,480,482,485,483,484,436,435,437,432,433,434,330,331,332,335,333,334,469,468,470,473,471,472,461,460,459,457,458,456,540,542,541,545,543,544,554,553,552,556,557,555,572,571,570,574,575,573,633,630,632,629,628,631,612,626,607,660,694,702,669,682,693,670,695,657,672,701,75,77,72,73,74,76,302,301,303,304,305,300,293,292,288,289,290,291,207,206,208,209,204,205,248,247,249,250,251,246,272,271,273,274,275,270,277,281,276,278,279,280,141,140,142,143,138,139,131,130,126,127,128,129,187,186,188,189,190,191,211,210,212,213,214,215,582,583,584,585,586,587,380,379,378,381,382,383,578,576,577,580,581,579,429,431,430,427,428,426,337,336,338,341,339,340,569,568,567,565,566,564,588,589,590,591,592,593,365,364,363,361,362,360,548,547,546,550,551,549,624,613,618,617,619,620,615,625,627,664,691,700,678,679,684,681,677,667,665,696,10,6,7,8,9,11,173,172,168,169,170,171,113,112,108,109,110,111,167,166,162,163,164,165,174,179,175,176,177,178,241,240,242,243,244,245,252,257,253,254,255,256,154,153,155,150,151,152,161,160,156,157,158,159,298,297,299,294,295,296,116,115,117,118,119,114,497,496,495,493,494,492,596,595,594,597,598,599,446,445,444,448,449,447,603,605,604,600,602,601,440,439,438,441,442,443,489,491,490,488,486,487,452,451,450,454,455,453,463,462,464,465,466,467,475,474,476,477,478,479,646,643,641,644,642,645,635,638,634,686,676,690,698,673,692,675,674,668,680,685,203,199,200,201,202,198,26,25,27,28,29,24,33,32,34,35,30,31,2,0,3,4,5,1,227,226,222,223,224,225,39,38,40,41,36,37,53,52,48,49,50,51,54,59,55,56,57,58,268,267,269,264,265,266,306,311,307,308,309,310,282,287,283,284,285,286,528,530,529,533,531,532,424,423,425,422,420,421,408,410,409,413,411,412,525,527,526,523,524,522,515,514,513,510,511,512,389,388,387,385,386,384,395,394,393,391,392,390,398,397,396,400,401,399,502,501,503,498,499,500,649,651,614,650,647,648,636,639,640,654,659,663,658,656,662,653,661,652,655,666 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#b487dc9287fe904f43c970fc4391e1719f627a657dc9e65b0768351b07a69a58, M = {84, 85, 86, 87, 88, 89, 126} 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 18:48:02 · history