Equation 677 Database

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Magma 058e3eb345d4…

magma 058e3eb345d4
Size
595
Isomorphism class hash
058e3eb345d4eff4f7e72788c16dd8495eee73b67678cc7e55e44686c1a7b937
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
2026-10-06 14:56:56
Display reorder
35,34,36,37,38,39,163,162,158,159,160,161,476,474,475,477,478,479,327,329,328,326,324,325,365,364,363,361,362,360,519,528,529,560,588,271,268,168,269,270,213,189,104,105,101,102,103,88,87,83,84,85,86,125,124,126,250,249,123,243,242,193,194,115,116,1,0,2,3,4,214,197,247,198,248,199,200,230,187,231,185,232,186,178,30,26,27,28,29,313,312,314,315,316,317,343,342,344,347,345,346,509,508,507,505,506,504,376,375,377,374,372,373,355,354,356,359,357,358,306,308,307,311,309,310,481,482,480,485,483,484,521,547,539,537,540,536,538,582,575,568,578,571,581,554,563,548,17,19,14,15,16,18,61,60,62,63,64,59,76,75,71,72,73,74,130,129,131,132,133,128,9,8,10,5,6,7,42,46,43,44,45,229,244,117,245,246,195,196,265,264,167,262,263,212,201,121,122,118,119,120,285,287,286,284,283,282,290,289,288,291,292,293,453,455,454,452,450,451,498,499,500,503,501,502,430,429,431,428,426,427,353,352,351,349,350,348,468,473,470,471,469,472,520,533,516,514,512,524,546,559,557,565,576,564,584,579,593,549,91,93,94,89,90,92,149,148,150,151,146,147,139,138,134,135,136,137,68,67,69,70,65,66,156,155,157,152,153,154,79,78,80,81,82,274,280,169,281,277,272,273,275,279,166,278,276,261,216,22,23,24,20,21,366,368,367,371,369,370,379,378,380,383,381,382,402,404,403,407,405,406,322,321,323,320,318,319,337,336,338,341,339,340,401,400,399,397,398,396,302,301,300,304,305,303,535,541,525,515,522,513,523,580,587,585,594,586,567,550,592,569,145,141,142,143,144,140,25,221,176,219,177,220,173,172,217,174,218,175,215,170,171,11,12,13,111,114,112,113,241,267,164,257,266,208,209,256,183,224,184,223,181,182,253,207,254,205,255,206,188,236,233,77,234,235,335,334,333,331,332,330,422,421,420,423,424,425,490,489,491,486,487,488,412,411,413,410,408,409,439,438,440,443,441,442,418,417,419,414,415,416,445,444,446,447,448,449,543,544,517,531,510,511,532,590,577,562,556,552,553,566,589,551,56,58,53,54,55,57,41,228,225,40,226,227,191,190,238,239,106,237,222,180,179,31,32,33,110,109,107,108,192,240,252,251,202,203,204,127,48,47,49,50,51,52,96,95,97,98,99,100,165,211,259,260,258,210,386,385,384,388,389,387,437,436,435,432,433,434,392,391,390,394,395,393,496,495,492,493,494,497,296,295,294,297,298,299,456,458,457,461,459,460,462,467,464,466,463,465,518,534,526,527,530,542,545,583,572,573,561,558,555,591,570,574 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#b487dc9287fe904f43c970fc4391e1719f627a657dc9e65b0768351b07a69a58, M = the submagma generated by {24, 30} (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 2026-10-06 14:56:57 · history