Equation 677 Database

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Magma 520c7b5bbd96…

magma 520c7b5bbd96
Size
381
Isomorphism class hash
520c7b5bbd96f9c092f62edb15e416e8bb5af6997b8486ea431fb2894a57ca86
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 23:16:23
Display reorder
380,83,286,75,93,98,88,211,216,220,226,231,236,316,317,315,313,314,312,170,175,165,156,161,150,196,201,205,181,186,190,30,275,25,40,45,35,101,290,106,110,115,120,241,246,251,257,262,267,19,20,270,0,5,10,51,63,65,71,280,57,126,136,131,145,140,296,336,361,331,345,366,355,340,375,351,371,82,285,76,92,97,87,210,215,221,225,230,235,311,309,310,308,306,307,171,176,166,155,160,151,195,200,206,180,185,191,32,277,27,42,47,37,100,291,105,111,116,121,242,247,252,256,260,265,16,23,274,2,7,12,50,62,66,70,281,58,125,135,130,146,141,295,337,360,330,346,365,356,342,376,350,370,81,289,79,90,95,85,214,219,224,229,234,239,327,328,329,324,325,326,174,179,169,159,164,154,199,204,209,184,189,194,34,279,29,44,49,39,104,294,109,114,119,124,240,245,250,255,261,266,18,21,271,1,6,11,54,61,69,74,284,56,129,139,134,149,144,299,339,364,334,348,369,359,344,379,354,374,80,287,77,91,96,86,212,217,222,227,232,237,304,305,303,300,302,301,172,177,167,157,162,152,197,202,207,182,187,192,31,276,26,41,46,36,102,292,107,112,117,122,243,248,253,258,263,268,15,22,272,3,8,13,52,60,67,72,282,55,127,137,132,147,142,297,335,362,332,347,367,357,341,377,352,372,84,288,78,94,99,89,213,218,223,228,233,238,320,318,319,323,321,322,173,178,168,158,163,153,198,203,208,183,188,193,33,278,28,43,48,38,103,293,108,113,118,123,244,249,254,259,264,269,17,24,273,4,9,14,53,64,68,73,283,59,128,138,133,148,143,298,338,363,333,349,368,358,343,378,353,373 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, M = {75} 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 23:16:24 · history