Equation 677 Database

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Magma a65cd4328843…

magma a65cd4328843
Size
707
Isomorphism class hash
a65cd43288436d0894cebc1d2adad472e238cc2fc47542707ae76d0d57e2f446
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 15:48:36
Display reorder
275,274,270,271,272,273,706,3,5,4,0,2,1,198,203,199,200,201,202,307,311,306,308,309,310,160,159,161,156,157,158,223,222,224,225,226,227,235,234,236,237,238,239,247,246,248,249,250,251,38,37,39,40,41,36,315,317,314,313,312,316,305,304,301,303,302,300,19,18,20,21,22,23,571,572,570,574,575,573,342,344,343,347,345,346,351,353,352,350,348,349,456,458,457,461,459,460,569,568,566,567,564,565,355,354,356,358,359,357,470,469,468,473,471,472,558,560,559,562,563,561,480,482,481,485,483,484,612,611,610,606,609,608,630,626,638,687,688,664,684,705,703,695,696,702,694,704,115,117,116,119,114,118,146,145,147,148,149,144,293,292,288,289,290,291,104,103,105,106,107,102,124,123,125,120,121,122,12,17,13,14,15,16,56,55,57,58,59,54,82,81,83,78,79,80,323,318,322,320,321,319,66,71,67,68,69,70,211,210,212,213,214,215,389,388,387,384,385,386,391,390,392,393,394,395,510,512,511,515,513,514,421,420,422,423,424,425,381,383,382,379,380,378,436,435,437,433,434,432,503,502,501,500,498,499,591,593,592,588,590,589,549,551,550,548,546,547,620,619,618,623,622,617,636,621,635,667,699,673,660,690,671,665,672,680,666,700,296,298,297,294,295,299,24,29,25,26,27,28,34,33,35,30,31,32,139,138,140,141,142,143,244,243,245,240,241,242,43,42,44,45,46,47,52,51,53,48,49,50,232,231,233,228,229,230,192,194,197,195,196,193,153,152,154,155,150,151,220,219,221,216,217,218,598,597,599,596,595,594,336,337,338,339,340,341,446,445,444,448,449,447,584,582,583,586,587,585,486,488,487,490,491,489,474,476,475,477,478,479,452,451,450,455,453,454,462,464,463,466,467,465,600,601,602,603,604,605,631,632,633,634,614,627,639,641,616,676,701,677,682,697,679,675,663,689,656,698,95,91,90,93,94,92,262,261,263,258,259,260,72,77,73,74,75,76,62,61,63,64,65,60,204,209,205,206,207,208,87,86,88,89,84,85,10,9,11,6,7,8,164,163,165,166,167,162,101,97,100,98,99,96,113,112,108,109,110,111,126,131,127,128,129,130,578,576,577,579,580,581,541,540,542,543,544,545,362,361,360,364,365,363,492,494,493,497,495,496,377,376,375,372,373,374,556,555,557,553,554,552,442,441,443,439,440,438,509,508,507,504,505,506,428,427,426,430,431,429,607,613,624,629,615,628,625,637,640,692,683,662,693,691,681,674,661,685,668,686,182,184,183,180,181,185,334,333,335,331,330,332,186,191,187,188,189,190,267,266,268,269,264,265,324,328,327,325,326,329,173,172,168,169,170,171,280,281,276,278,279,277,257,256,252,253,254,255,283,285,282,286,287,284,179,178,174,175,176,177,135,134,136,137,132,133,402,404,403,406,407,405,396,398,397,401,399,400,419,418,417,415,416,414,409,408,410,411,412,413,369,371,370,367,368,366,516,518,517,519,520,521,523,522,524,526,527,525,529,528,530,533,531,532,534,536,535,539,537,538,643,646,642,649,644,650,647,648,645,657,670,655,658,678,652,654,653,659,651,669 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#10d95f4d62da29d597cabb26c5d7a2889acb76e08f2897cdd164594c6bfbc5c4, M = {6, 7, 8, 9, 10, 11, 143} 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 15:48:38 · history