Equation 677 Database

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Magma 3be21825550b…

magma 3be21825550b
Size
595
Isomorphism class hash
3be21825550ba9f4bb2f6f93b51ddd315b72c16354abe52b5d76c65e3348e211
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 22:09:30
Display reorder
296,295,294,297,298,299,377,376,378,379,380,381,411,410,409,407,408,406,401,400,402,403,404,405,275,274,270,271,272,273,539,541,538,540,594,477,478,351,479,480,444,451,365,366,367,368,369,342,341,422,338,339,340,415,417,416,481,482,426,505,484,445,446,358,357,390,392,391,388,389,492,454,496,463,495,452,453,113,112,108,109,110,111,74,73,75,76,77,72,133,132,134,135,136,137,81,80,82,83,78,79,162,167,163,164,165,166,2,0,3,4,5,1,65,64,60,61,62,63,42,47,43,44,45,46,56,55,57,58,59,54,535,543,532,529,516,524,519,557,559,554,561,560,570,553,551,558,290,289,288,293,291,292,279,281,280,278,276,277,394,393,395,396,397,398,300,302,301,304,305,303,334,333,332,335,336,337,354,353,352,356,355,483,468,287,469,467,436,437,157,156,158,159,160,161,216,221,217,218,219,220,70,69,71,66,67,68,249,248,250,251,246,247,268,267,269,264,265,266,119,118,114,115,116,117,88,87,89,84,85,86,173,172,168,169,170,171,52,51,53,48,49,50,537,545,531,526,517,522,523,583,569,572,556,582,593,590,573,566,347,346,348,344,345,343,286,427,285,283,284,282,385,387,386,384,382,383,373,375,374,371,372,370,330,329,331,328,326,327,428,430,429,431,432,509,506,399,507,508,493,494,128,127,129,130,131,126,256,255,257,252,253,254,231,230,232,233,228,229,223,222,224,225,226,227,239,238,234,235,236,237,141,140,142,143,138,139,243,242,244,245,240,241,122,121,123,124,125,120,153,152,154,155,150,151,548,547,546,511,510,521,512,591,563,588,586,565,587,585,564,562,322,321,320,325,323,324,421,503,462,504,461,502,457,464,499,456,498,455,470,438,439,308,306,307,362,361,360,359,497,485,363,487,486,448,447,488,440,471,441,472,442,443,200,199,201,202,203,198,149,148,144,145,146,147,19,18,20,21,22,23,261,260,262,263,258,259,96,101,97,98,99,100,36,41,37,38,39,40,103,102,104,105,106,107,180,185,181,182,183,184,209,208,204,205,206,207,534,542,533,514,527,528,513,589,579,567,550,580,568,592,576,552,314,313,312,311,309,310,349,474,473,350,475,476,449,450,491,490,364,489,500,459,458,413,414,412,423,420,419,418,460,501,465,466,433,434,435,425,315,424,316,317,318,319,92,91,93,94,95,90,192,197,193,194,195,196,186,191,187,188,189,190,7,6,8,9,10,11,26,25,27,28,29,24,213,212,214,215,210,211,175,174,176,177,178,179,33,32,34,35,30,31,17,16,12,13,14,15,536,544,530,525,515,520,518,578,571,575,577,549,584,574,555,581 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#f44078deebe7730562c927e2829a32c42b90cd1087b6200dbe445a4d4d2f9fa6, 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 22:09:31 · history