Equation 677 Database

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Magma 9201d78a4901…

magma 9201d78a4901
Size
595
Isomorphism class hash
9201d78a4901aa117b49c71e864e9f9f5778c9025d16a7952698708444612e17
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 15:53:46
Display reorder
66,68,67,71,69,70,108,110,109,113,111,112,138,140,139,142,143,141,420,425,421,422,423,424,489,488,490,491,486,487,519,526,533,581,584,170,169,168,171,172,173,17,16,15,12,13,14,40,39,41,38,36,37,77,76,75,72,73,74,187,195,191,183,256,253,237,236,238,239,240,249,235,248,247,234,232,233,93,95,94,91,92,90,337,336,338,339,340,341,335,334,330,331,332,333,408,413,409,410,411,412,465,464,466,467,462,463,269,268,264,265,266,267,475,474,476,477,478,479,483,482,484,485,480,481,407,406,402,403,404,405,515,552,524,550,538,520,511,543,580,568,592,586,593,583,585,571,211,213,212,209,210,208,245,244,246,243,241,242,252,255,182,192,184,188,151,150,152,155,153,154,107,106,105,103,104,102,60,62,61,65,63,64,147,149,148,146,144,145,196,198,197,200,201,199,398,397,399,400,401,396,450,455,451,452,453,454,427,426,428,429,430,431,504,509,505,506,507,508,443,442,438,439,440,441,414,419,415,416,417,418,283,282,284,285,286,287,280,279,281,276,277,278,542,534,544,518,546,535,551,528,590,575,572,570,576,573,578,565,43,42,44,47,45,46,83,82,81,78,79,80,31,30,32,35,33,34,5,4,3,1,0,2,7,6,8,9,10,11,118,117,119,114,115,116,22,21,23,19,18,20,161,160,159,156,157,158,322,321,323,318,319,320,448,447,449,444,445,446,437,436,432,433,434,435,294,299,295,296,297,298,503,502,498,499,500,501,383,382,378,379,380,381,388,387,389,384,385,386,358,357,359,354,355,356,529,513,536,527,516,512,521,510,594,589,558,563,555,582,559,554,207,206,205,202,203,204,225,224,223,220,221,222,251,257,181,194,186,190,135,137,136,133,134,132,130,129,131,126,127,128,121,120,122,123,124,125,176,175,174,178,179,177,166,165,167,164,162,163,288,293,289,290,291,292,309,308,310,311,306,307,368,367,369,370,371,366,315,314,316,317,312,313,365,364,360,361,362,363,305,304,300,301,302,303,473,472,468,469,470,471,460,459,461,456,457,458,541,539,537,530,545,532,548,531,591,560,561,587,567,556,579,566,97,96,98,101,99,100,29,28,27,24,25,26,53,52,51,48,49,50,86,85,84,87,88,89,185,193,189,180,254,250,230,229,231,226,227,228,219,218,217,215,216,214,59,58,57,54,55,56,326,325,327,328,329,324,375,374,376,377,372,373,497,496,492,493,494,495,272,271,273,274,275,270,260,258,261,262,263,259,395,394,390,391,392,393,353,352,348,349,350,351,345,344,346,347,342,343,523,547,517,549,525,522,514,540,553,569,588,564,577,574,557,562 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#f04ca8125d7ce546c7552606527b36663a07f654279810fba8dfdb3271b338ee, M = the submagma generated by {0, 24} (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 15:53:47 · history