Equation 677 Database

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Magma e033fd1e8ac0…

magma e033fd1e8ac0
Size
595
Isomorphism class hash
e033fd1e8ac025f67538acc84bb357df0f0562cfc1022f5943753b38dd2e0cc6
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
2026-10-09 00:22:05
Display reorder
300,301,302,305,303,304,338,337,339,340,341,336,419,418,414,415,416,417,345,344,346,347,342,343,439,438,440,441,442,443,555,589,590,588,587,183,182,181,179,180,178,208,210,209,212,213,211,42,41,43,46,44,45,87,86,88,83,84,85,193,195,194,191,192,190,234,233,232,236,237,235,101,103,102,106,104,105,57,56,58,55,53,54,268,267,266,264,265,263,121,123,122,119,120,118,379,378,380,381,382,383,360,365,361,362,363,364,459,458,460,461,456,457,470,469,471,472,473,468,311,310,307,306,308,309,412,411,413,408,409,410,514,532,524,522,521,538,536,542,550,556,577,569,562,576,575,586,2,0,1,4,5,3,49,48,47,50,51,52,165,164,163,160,161,162,109,111,110,108,107,275,253,255,254,251,252,250,114,113,112,116,117,115,174,173,172,176,177,175,147,146,145,142,143,144,187,189,188,186,184,185,203,202,204,207,205,206,369,368,370,371,366,367,321,320,322,323,318,319,494,493,495,496,497,492,506,504,507,508,509,505,445,444,446,447,448,449,425,424,420,421,422,423,512,537,515,523,527,530,543,535,553,559,573,568,561,574,580,581,15,14,16,11,12,13,153,152,151,148,149,150,96,95,97,100,98,99,35,37,36,40,38,39,219,218,217,214,215,216,299,298,297,294,296,295,90,89,91,92,93,94,249,248,247,244,245,246,238,240,239,243,241,242,272,274,273,270,271,269,334,333,335,330,331,332,327,326,328,329,324,325,474,479,475,476,477,478,484,483,485,480,481,482,377,376,372,373,374,375,389,388,384,385,386,387,513,545,516,529,518,534,539,554,551,557,592,570,564,591,594,593,31,30,29,33,34,32,258,257,259,262,260,261,222,221,220,223,224,225,9,256,10,8,6,7,228,227,226,229,230,231,26,28,27,25,23,24,76,75,74,72,73,71,129,128,127,124,125,126,19,18,17,21,22,20,130,132,131,134,135,133,391,390,392,393,394,395,434,433,435,436,437,432,498,503,499,500,501,502,467,466,462,463,464,465,354,359,355,356,357,358,317,316,312,313,314,315,510,533,517,519,526,544,541,540,552,560,572,566,565,571,578,579,198,197,196,200,201,199,276,277,278,281,279,280,291,293,292,288,290,289,287,286,285,282,284,283,62,64,63,60,61,59,159,158,157,155,156,154,79,78,77,81,82,80,70,69,68,65,66,67,166,168,167,171,169,170,136,138,137,140,141,139,402,407,403,404,405,406,427,426,428,429,430,431,451,455,450,452,453,454,488,487,489,490,491,486,400,399,401,396,397,398,351,350,352,353,348,349,511,547,525,520,528,546,531,548,549,558,582,567,563,583,584,585 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 {18, 72} (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 2026-10-09 00:22:06 · history