Equation 677 Database

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Magma 516a95e0b6ae…

magma 516a95e0b6ae
Size
595
Isomorphism class hash
516a95e0b6aec70d59793735f217253de293d2c592671b6149ae02e3b9cd8d59
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 19:29:24
Display reorder
101,100,102,97,98,99,112,111,113,116,119,110,46,45,41,42,43,44,19,22,115,118,20,21,441,443,442,439,440,438,528,567,578,573,565,249,250,180,247,248,251,179,150,146,147,148,149,131,130,126,127,128,129,117,114,109,218,219,170,212,214,213,167,94,95,62,61,63,59,60,194,176,230,227,228,229,175,185,184,181,156,182,183,420,422,421,423,424,425,316,315,317,313,314,312,486,488,487,489,490,491,456,458,457,459,460,461,498,497,499,500,501,502,485,484,483,480,481,482,394,393,395,390,391,392,370,369,371,368,366,367,549,548,512,534,535,533,530,537,592,571,593,586,556,576,551,582,52,48,47,50,51,49,68,67,69,64,65,66,36,35,37,38,39,40,28,27,23,24,25,26,70,75,71,72,73,74,93,92,89,90,91,211,201,164,202,203,204,163,220,245,171,242,244,243,503,496,495,494,492,493,283,282,284,280,281,279,275,274,273,278,276,277,507,506,505,504,508,509,465,467,466,464,462,463,310,309,311,308,306,307,346,345,347,342,343,344,433,432,434,437,435,436,532,531,516,550,547,526,523,510,558,579,580,561,570,569,577,557,80,82,81,84,79,83,5,4,0,1,2,3,55,54,56,57,58,53,140,139,135,136,137,138,34,33,29,30,31,32,152,151,153,154,155,263,257,253,258,255,256,246,261,260,252,259,254,262,468,470,469,471,472,473,267,269,268,270,271,272,403,402,404,406,407,405,409,408,410,412,413,411,401,400,399,397,398,396,320,319,318,321,322,323,429,431,430,428,426,427,385,384,386,389,387,388,529,517,525,514,522,540,515,524,574,554,564,590,594,584,591,555,16,12,17,14,15,13,18,189,186,187,157,188,191,158,192,159,193,190,200,199,162,78,76,77,143,142,144,145,240,241,174,225,226,223,173,224,166,207,208,209,210,165,237,236,238,178,239,235,334,333,335,331,332,330,479,478,477,476,474,475,365,364,363,362,360,361,326,325,324,329,327,328,285,287,286,288,289,290,298,297,299,264,266,265,444,446,445,449,447,448,341,340,339,336,337,338,544,546,520,539,519,511,527,518,552,589,553,568,585,560,588,559,7,9,8,11,6,10,141,234,231,177,232,233,195,161,196,197,160,198,222,221,172,132,133,134,85,88,86,87,205,206,217,216,168,215,169,96,125,124,120,121,122,123,107,106,108,103,104,105,358,357,359,355,356,354,379,378,380,382,383,381,455,454,453,452,450,451,349,348,350,352,353,351,304,303,305,300,301,302,294,296,295,292,293,291,414,416,415,419,417,418,376,375,377,374,372,373,536,538,541,543,545,513,542,521,587,566,563,581,572,583,575,562 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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 = the submagma generated by {24, 36} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 19:29:25 · history