Equation 677 Database

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Magma 07f88b901236…

magma 07f88b901236
Size
707
Isomorphism class hash
07f88b901236d636522e9951e5c3a0fed0b5d4820cc0f46b5b83542f4a5d14c3
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 14:03:46
Display reorder
484,483,485,481,482,480,641,195,196,197,192,193,194,22,21,23,18,19,20,79,78,80,81,82,83,41,40,36,37,38,39,259,258,260,261,262,263,153,152,154,155,150,151,251,250,246,247,248,249,211,210,212,213,214,215,292,291,293,288,289,290,278,277,279,280,281,276,359,354,355,356,358,357,223,222,224,225,226,227,473,472,471,470,468,469,511,510,512,513,514,515,424,423,425,422,420,421,458,457,456,461,459,460,443,442,441,440,438,439,507,509,508,504,505,506,360,361,362,365,363,364,376,375,377,374,372,373,608,610,606,607,611,609,634,613,682,655,647,658,688,684,701,699,698,706,703,702,2,3,4,5,1,0,15,14,16,17,12,13,165,164,166,167,162,163,47,46,42,43,44,45,308,307,309,310,311,306,319,318,320,321,322,323,182,181,183,184,185,180,145,144,146,147,148,149,137,136,132,133,134,135,119,118,114,115,116,117,131,130,126,127,128,129,110,109,111,112,113,108,537,539,538,534,535,536,501,503,502,500,498,499,532,531,533,530,528,529,571,570,572,568,569,567,545,544,543,542,540,541,492,494,493,495,496,497,419,418,417,414,415,416,601,602,600,604,605,603,618,617,619,621,620,622,630,623,695,652,663,653,683,669,696,666,697,705,681,690,296,297,298,299,294,295,328,327,329,324,325,326,245,244,240,241,242,243,102,107,103,104,105,106,337,336,338,339,340,341,342,347,343,344,345,346,51,50,52,53,48,49,312,317,313,314,315,316,158,157,159,160,161,156,72,77,73,74,75,76,8,7,9,10,11,6,190,189,191,186,187,188,388,387,389,385,386,384,371,370,369,367,368,366,574,573,575,565,566,564,391,407,390,394,392,393,583,584,582,585,586,587,403,402,401,406,404,405,383,382,381,378,379,380,410,409,408,411,412,413,615,616,614,625,624,626,633,627,677,665,664,654,672,678,693,692,680,700,670,691,32,33,34,35,30,31,25,24,26,27,28,29,175,174,176,177,178,179,121,120,122,123,124,125,332,331,333,334,335,330,138,143,139,140,141,142,302,301,303,304,305,300,170,169,171,172,173,168,349,353,348,350,351,352,56,55,57,58,59,54,237,236,238,239,234,235,62,61,63,64,65,60,576,578,577,579,580,581,563,562,561,559,560,558,548,547,546,549,550,551,553,552,554,556,557,555,395,397,396,398,399,400,598,597,599,594,596,595,592,591,593,590,589,588,486,488,487,490,491,489,629,612,628,631,632,635,643,644,668,674,649,675,676,667,687,686,679,704,689,694,232,233,228,229,230,231,67,66,68,69,70,71,96,101,97,98,99,100,90,95,91,92,93,94,286,285,287,282,283,284,275,274,270,271,272,273,86,85,87,88,89,84,266,265,267,264,269,268,207,206,208,209,204,205,255,254,256,257,252,253,217,216,218,219,220,221,199,198,200,201,202,203,426,428,427,429,430,431,433,432,434,435,436,437,519,521,520,517,518,516,467,466,465,464,462,463,453,455,454,450,451,452,475,474,476,478,479,477,527,526,525,522,523,524,444,446,445,448,449,447,640,638,636,637,639,642,645,646,673,651,648,650,671,662,661,659,660,685,656,657 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#5d364ad3474cdcd7c6d5defafd2fd9bfd394ea971d15e95ed0d16a1c5a75c76d, M = {96, 97, 98, 99, 100, 101, 127} 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 14:03:47 · history