Equation 677 Database

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Magma 5b07b7a12877…

magma 5b07b7a12877
Size
707
Isomorphism class hash
5b07b7a12877b289a5c5ffcba0fa8e2961fbac472593fba97a0cca613b21712e
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
2026-10-08 01:53:18
Display reorder
61,60,62,63,64,65,706,299,298,294,295,296,297,245,241,240,242,243,244,217,216,218,219,220,221,234,235,236,237,238,239,167,166,162,163,164,165,288,289,290,291,292,293,188,187,189,190,191,186,4,3,5,1,0,2,9,8,10,11,6,7,304,305,301,302,303,300,327,328,545,325,326,324,339,338,340,336,337,335,474,473,475,476,477,478,490,489,488,487,485,486,372,371,373,376,374,375,500,502,501,497,498,499,383,385,384,386,387,388,395,397,396,400,399,398,540,539,541,542,543,544,528,527,529,531,532,530,609,611,610,612,613,608,640,637,642,638,701,678,693,704,700,683,699,694,705,703,144,149,145,146,147,148,253,254,255,256,257,252,246,251,247,248,249,250,152,151,153,154,155,150,271,272,270,273,274,275,115,114,116,117,118,119,277,281,276,278,279,280,207,206,208,209,204,205,88,87,89,84,85,86,111,110,112,113,108,109,362,364,363,360,361,359,546,547,548,550,551,549,506,508,507,505,503,504,430,429,428,427,425,426,415,414,413,416,417,418,423,422,424,420,421,419,431,433,432,434,435,436,408,407,409,412,410,411,404,406,405,403,401,402,553,554,552,555,556,557,627,629,626,625,622,623,628,621,624,633,702,696,695,682,671,663,679,667,681,685,125,124,120,121,122,123,34,35,30,31,32,33,137,136,132,133,134,135,131,130,126,127,128,129,175,174,176,177,178,179,182,181,183,184,185,180,15,14,16,17,12,13,21,20,22,23,18,19,28,27,29,24,25,26,159,158,160,161,156,157,465,464,466,463,461,462,558,559,560,562,563,561,348,347,349,350,351,352,353,355,354,356,357,358,314,313,312,315,316,317,307,308,306,309,310,311,525,524,526,522,523,521,366,365,367,370,368,369,564,565,566,567,568,569,571,572,570,573,574,575,632,630,636,631,607,606,639,635,641,634,691,692,686,687,664,673,672,674,680,697,284,282,285,286,287,283,81,82,83,78,79,80,74,73,75,76,77,72,68,67,69,70,71,66,106,105,107,102,103,104,97,96,98,99,100,101,93,92,94,95,90,91,233,232,228,229,230,231,224,223,225,226,227,222,143,142,138,139,140,141,453,452,454,451,449,450,604,603,605,600,602,601,518,520,519,517,515,516,446,448,447,443,444,445,578,576,577,579,580,581,457,456,455,460,458,459,585,587,586,583,582,584,598,597,599,596,595,594,438,437,439,440,441,442,591,593,592,589,588,590,647,644,648,645,646,643,651,653,650,654,698,677,684,690,675,668,676,670,689,688,43,42,44,45,46,47,55,56,57,58,59,54,215,214,210,211,212,213,259,263,258,260,261,262,51,50,52,53,48,49,193,192,194,195,196,197,265,269,264,266,267,268,198,203,199,200,201,202,41,40,36,37,38,39,172,171,173,168,169,170,533,535,534,537,538,536,513,512,514,510,511,509,378,377,379,380,381,382,392,394,393,389,390,391,484,483,482,479,480,481,492,491,493,495,496,494,467,469,468,470,471,472,333,332,334,331,329,330,344,346,345,343,341,342,321,323,322,318,319,320,618,649,614,615,616,619,652,617,620,655,666,660,662,665,657,658,659,656,661,669 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#33d45c5563bf4abb244f69cfa51749fb5a869f311e4fb00d8e6c25812252a226, M = {54, 55, 56, 57, 58, 59, 145} 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 2026-10-08 01:53:19 · history