Equation 677 Database

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Magma 43aea79ee44f…

magma 43aea79ee44f
Size
381
Isomorphism class hash
43aea79ee44fbafc9fb91af57f094a62d5c46b5107fb4918352f7e41eec682ca
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 23:15:44
Display reorder
380,178,173,183,158,163,168,28,33,38,43,48,298,233,238,288,218,223,228,301,300,302,303,304,305,73,63,68,58,53,243,258,248,253,278,263,268,83,87,78,283,98,93,123,118,293,113,103,108,203,208,213,188,193,198,18,273,15,17,16,19,133,128,138,143,148,153,333,373,353,338,358,342,368,378,363,348,179,174,184,159,164,169,29,34,39,44,49,299,234,239,289,219,224,229,315,316,314,312,313,311,74,64,69,59,54,244,259,249,254,279,264,269,84,88,79,284,99,94,124,119,294,114,104,109,204,209,214,189,194,199,23,274,20,22,21,24,134,129,139,144,149,154,334,374,354,339,359,343,369,379,364,349,177,172,182,157,162,167,25,31,36,40,45,296,232,237,287,217,222,227,307,329,306,309,310,308,71,61,66,55,50,240,256,246,251,275,260,265,81,86,77,281,95,90,122,117,292,112,102,107,202,207,212,187,192,197,13,272,10,12,11,14,132,127,137,142,147,152,332,372,352,337,356,341,366,375,362,347,176,171,180,156,161,166,26,30,35,41,46,295,231,235,285,216,221,225,321,322,320,318,319,317,72,60,65,56,51,241,255,245,250,276,261,266,80,89,76,282,97,92,121,116,290,111,101,106,201,206,211,185,190,195,0,271,4,3,2,1,130,125,135,141,146,150,331,371,350,335,355,340,365,376,360,345,175,170,181,155,160,165,27,32,37,42,47,297,230,236,286,215,220,226,325,323,324,328,326,327,70,62,67,57,52,242,257,247,252,277,262,267,82,85,75,280,96,91,120,115,291,110,100,105,200,205,210,186,191,196,8,270,5,7,6,9,131,126,136,140,145,151,330,370,351,336,357,344,367,377,361,346 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, 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 23:15:45 · history