Equation 677 Database

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Magma 134d8263364b…

magma 134d8263364b
Size
381
Isomorphism class hash
134d8263364bd2ca17f3cba59cb1c676a63a4a687f17d0ed82e5ce0c61923f84
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:22:39
Display reorder
380,172,167,162,182,187,177,313,314,312,316,317,315,247,252,257,262,267,272,222,227,217,236,242,231,292,27,32,24,11,16,43,47,38,57,61,52,66,71,275,80,85,76,107,297,112,92,97,102,137,142,132,122,127,117,207,212,287,192,197,202,4,282,5,157,146,151,332,347,342,355,352,337,362,377,367,370,170,165,160,180,185,176,310,311,309,307,308,306,246,251,255,261,266,270,221,226,215,238,240,232,291,26,30,21,10,15,41,45,35,56,62,51,67,72,277,82,87,77,105,296,110,90,96,101,136,141,131,121,126,116,205,210,286,191,196,201,0,281,1,155,147,152,330,345,341,357,350,336,361,376,366,371,173,168,163,183,188,178,327,328,329,324,325,326,248,253,258,263,268,273,223,228,218,237,243,233,293,28,33,22,13,18,44,48,39,58,63,53,68,73,278,83,88,78,108,298,113,93,98,103,138,143,133,123,128,118,208,213,288,193,198,203,6,283,7,158,145,150,333,348,343,358,353,338,363,378,368,372,171,166,161,181,186,175,323,321,322,320,318,319,245,250,256,260,265,271,220,225,216,235,241,230,290,25,31,20,12,17,42,46,37,55,60,50,65,70,276,81,86,75,106,295,111,91,95,100,135,140,130,120,125,115,206,211,285,190,195,200,2,280,3,156,148,153,331,346,340,356,351,335,360,375,365,374,174,169,164,184,189,179,305,303,304,302,301,300,249,254,259,264,269,274,224,229,219,239,244,234,294,29,34,23,14,19,40,49,36,59,64,54,69,74,279,84,89,79,109,299,114,94,99,104,139,144,134,124,129,119,209,214,289,194,199,204,8,284,9,159,149,154,334,349,344,359,354,339,364,379,369,373 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60, M = {76} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:22:40 · history