Equation 677 Database

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Magma fa76734b4e62…

magma fa76734b4e62
Size
595
Isomorphism class hash
fa76734b4e628331c708ec2fb37e79266d70f6db851cee218832589605ef847e
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 08:20:46
Display reorder
90,92,91,94,95,93,28,27,29,26,24,25,87,89,88,84,85,86,432,437,433,434,435,436,459,458,460,461,456,457,523,524,513,579,572,96,98,97,99,100,101,134,133,132,129,130,131,121,120,122,117,118,119,114,116,115,113,111,112,195,191,187,183,256,253,223,222,224,220,221,249,247,248,246,243,244,245,137,136,135,138,139,140,455,454,450,451,452,453,390,395,391,392,393,394,268,267,269,264,265,266,304,303,305,300,301,302,447,446,448,449,444,445,362,361,363,364,365,360,326,325,327,328,329,324,397,396,398,399,400,401,525,552,527,543,530,531,528,548,558,593,564,570,555,574,577,578,225,227,226,228,229,230,237,239,238,241,242,240,251,255,182,184,188,192,30,32,31,35,33,34,82,81,83,79,80,78,160,159,161,162,163,164,42,44,43,46,47,45,196,198,197,200,201,199,478,477,479,474,475,476,384,389,385,386,387,388,416,415,417,418,419,414,504,509,505,506,507,508,403,402,404,405,406,407,468,473,469,470,471,472,258,259,260,261,262,263,333,332,334,335,330,331,549,516,514,522,551,544,542,535,591,581,576,569,586,563,573,582,7,6,8,10,11,9,65,64,63,60,61,62,41,40,39,37,38,36,127,126,128,123,124,125,3,5,4,1,0,2,72,74,73,77,75,76,103,102,104,107,105,106,174,176,175,178,179,177,320,319,321,322,323,318,487,486,488,489,490,491,467,466,462,463,464,465,422,421,423,424,425,420,503,502,498,499,500,501,376,375,377,372,373,374,430,429,431,426,427,428,279,278,280,281,276,277,511,526,529,510,519,539,515,521,594,584,575,580,571,585,590,557,219,218,217,216,214,215,204,203,202,205,206,207,252,257,181,186,190,194,53,52,51,49,50,48,143,142,141,146,144,145,148,147,149,150,151,152,165,167,166,169,170,168,108,110,109,172,173,171,356,355,357,358,359,354,353,352,348,349,350,351,368,367,369,370,371,366,309,308,310,311,306,307,294,299,295,296,297,298,440,439,441,442,443,438,345,344,346,347,342,343,291,290,292,293,288,289,547,536,517,532,545,537,541,533,592,565,559,588,562,583,554,556,20,19,18,23,21,22,59,58,57,54,55,56,17,16,15,13,14,12,66,68,67,71,69,70,193,189,185,180,254,250,236,235,234,232,233,231,209,208,210,213,211,212,156,158,157,154,155,153,274,273,275,270,271,272,496,495,497,492,493,494,480,485,481,482,483,484,286,285,287,282,283,284,410,409,411,412,413,408,341,340,336,337,338,339,317,316,312,313,314,315,378,383,379,380,381,382,512,546,520,540,518,534,538,550,553,561,560,587,568,589,567,566 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#54e3a19f93137e404c924a9b37966faa8299b270c95916aef4ed0fa8730aa82d, M = the submagma generated by {6, 12} (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 08:20:48 · history