Equation 677 Database

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Magma e015c8b61c98…

magma e015c8b61c98
Size
595
Isomorphism class hash
e015c8b61c98855fe461fb7eae61c538e05d35fa41bb2663297ebd8340df3f06
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 01:20:57
Display reorder
328,330,329,326,420,327,293,292,291,288,289,290,359,358,360,357,355,356,284,283,282,287,285,286,110,109,111,112,113,108,528,535,513,510,563,489,490,397,488,487,455,456,401,402,400,398,399,388,389,424,386,387,385,426,414,417,497,498,415,469,468,438,439,319,318,374,376,375,377,378,480,448,481,447,501,446,463,43,42,44,45,46,47,29,28,24,25,26,27,141,140,142,137,138,139,128,127,129,130,125,126,36,39,41,40,37,38,184,183,185,180,181,182,33,32,34,35,30,31,56,55,57,58,59,54,62,61,63,64,65,60,540,544,518,521,516,522,526,566,577,567,576,549,551,550,575,554,299,297,296,294,295,298,383,382,384,381,379,380,321,320,322,325,323,324,337,336,335,334,332,333,362,364,363,365,366,367,338,340,339,341,342,473,475,343,476,474,442,443,120,121,178,122,123,124,226,225,227,222,223,224,215,214,210,211,212,213,255,254,256,257,252,253,246,251,247,248,249,250,52,51,53,48,49,50,136,135,131,132,133,134,160,159,155,156,157,158,71,70,66,67,68,69,514,524,538,539,515,517,545,564,555,585,581,587,591,584,572,565,368,369,371,372,373,370,354,353,352,350,351,419,306,308,307,310,311,309,305,304,303,302,300,301,280,279,281,277,278,276,428,430,429,431,432,509,507,427,508,506,504,505,232,231,233,228,229,230,243,242,244,245,240,241,219,218,220,221,216,217,234,239,235,236,237,238,86,85,87,88,89,84,260,259,261,262,263,258,266,265,267,268,269,264,164,163,165,166,161,162,119,118,114,115,116,117,512,548,546,533,547,536,534,589,592,586,570,590,560,593,573,588,348,349,345,346,344,347,416,500,462,499,461,502,459,460,496,434,465,433,484,453,454,391,392,390,396,395,394,393,485,486,331,472,471,441,440,470,450,482,449,483,452,451,73,72,74,75,76,77,91,90,92,93,94,95,18,23,19,20,21,22,273,272,274,275,270,271,6,11,7,8,9,10,154,153,149,150,151,152,201,200,202,203,198,199,4,3,5,1,0,2,106,105,107,102,103,104,537,542,532,527,519,531,525,594,571,556,562,559,553,580,569,557,313,314,316,317,315,312,413,494,495,412,492,493,445,444,479,477,361,478,491,457,458,410,411,409,423,425,422,421,464,503,466,467,437,435,436,418,406,408,407,405,403,404,12,17,13,14,15,16,189,188,190,191,186,187,195,194,196,197,192,193,168,167,169,170,171,172,175,174,176,177,179,173,208,206,209,207,204,205,145,144,146,147,148,143,78,83,79,80,81,82,96,101,97,98,99,100,529,530,511,541,523,520,543,583,582,579,561,578,574,568,558,552 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#21508ce76d8339c8cc8a9db508194b7933fb8eb19570d11d640cb6bc14178d14, M = the submagma generated by {12, 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 01:20:58 · history