Equation 677 Database

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Magma 0787389a1abf…

magma 0787389a1abf
Size
595
Isomorphism class hash
0787389a1abfea63668203d848959077a997a9eb57b31624b525141cdd32b699
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 01:23:33
Display reorder
139,138,140,141,142,143,239,238,234,235,236,237,342,344,343,341,339,340,376,378,377,380,381,379,330,329,328,325,326,327,510,513,515,553,574,212,214,213,210,211,215,264,269,265,266,267,268,278,277,279,280,281,276,34,33,35,30,31,32,89,88,84,85,86,87,161,160,156,157,158,159,40,39,41,36,37,38,97,96,98,99,100,101,129,128,130,131,126,127,209,208,204,205,206,207,388,390,389,391,392,393,402,401,400,403,404,405,338,337,336,334,335,333,321,323,322,318,319,320,495,493,509,508,492,494,332,467,429,466,428,465,526,532,512,511,518,517,579,557,564,585,563,555,566,561,562,583,176,178,177,174,175,179,181,180,182,183,184,185,134,133,135,136,137,132,201,200,202,203,198,199,60,65,61,62,63,64,26,25,27,28,29,24,227,226,222,223,224,225,308,307,309,310,311,306,55,54,56,57,58,59,80,79,81,82,83,78,459,458,419,497,501,496,486,499,487,484,485,483,504,469,500,468,430,431,488,451,450,449,447,448,383,382,384,386,387,385,352,474,442,473,441,472,541,534,514,523,539,540,565,543,545,551,593,569,559,546,544,560,186,188,187,190,191,189,193,192,194,195,196,197,2,0,3,4,5,1,231,230,232,233,228,229,298,297,299,294,295,296,20,19,21,22,23,18,283,282,284,285,286,287,166,165,167,162,163,164,220,219,221,216,217,218,173,172,168,169,170,171,350,349,351,347,348,346,358,357,356,353,354,355,410,411,412,413,414,415,313,312,314,316,317,315,482,481,507,409,506,480,479,408,478,505,477,407,535,536,528,522,521,527,571,588,589,586,590,587,567,558,568,572,66,68,67,70,71,69,52,51,53,48,49,50,93,92,94,95,90,91,14,13,15,16,17,12,253,252,254,255,256,257,115,114,116,117,118,119,289,288,290,291,292,293,8,7,9,10,11,6,108,113,109,110,111,112,248,247,249,250,251,246,489,453,452,417,418,416,371,370,372,375,373,374,363,362,361,359,360,443,438,470,345,471,440,439,364,366,365,367,368,369,422,420,502,498,503,421,524,533,542,520,525,519,573,594,581,552,547,550,575,578,548,576,302,304,303,300,301,305,242,241,243,244,245,240,107,106,102,103,104,105,258,263,259,260,261,262,47,46,42,43,44,45,145,144,146,147,148,149,77,76,72,73,74,75,270,275,271,272,273,274,151,150,152,153,154,155,124,123,125,120,121,122,491,457,456,455,454,490,460,424,423,324,425,461,435,437,436,434,432,433,444,475,406,476,446,445,397,399,398,394,395,396,331,462,426,464,427,463,537,538,529,516,531,530,582,554,592,580,584,570,591,549,556,577 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#be842e4d65ca083f5f61a36963819b0aa7d50180968070250538ce7f22ff68d2, M = the submagma generated by {12, 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 2026-10-09 01:23:34 · history