Equation 677 Database

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Magma c58551521299…

magma c58551521299
Size
381
Isomorphism class hash
c585515212991dd261c7764e0df02af695f127abb01d633705893a2e911da47c
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 23:45:16
Display reorder
380,143,148,293,138,128,133,21,12,17,267,27,32,321,322,323,318,319,320,0,7,278,61,66,70,53,58,273,38,43,48,262,252,257,247,237,242,177,182,185,190,195,201,288,103,108,113,118,123,297,167,172,162,152,157,231,222,225,217,207,211,89,99,93,83,78,283,358,343,363,353,367,371,348,377,333,337,144,149,294,139,129,134,20,13,18,268,28,33,300,302,301,304,305,303,9,8,279,64,69,74,54,59,274,39,44,49,263,253,258,248,238,243,178,183,188,193,198,203,289,104,109,114,119,124,298,168,173,163,153,158,233,223,228,218,208,213,88,98,94,84,79,284,359,344,364,354,368,372,349,378,332,338,141,146,290,136,126,131,22,11,15,265,26,31,328,329,327,325,326,324,2,3,275,62,67,72,50,55,271,36,41,46,260,250,255,246,235,240,176,181,186,191,196,200,285,100,105,110,116,121,296,165,170,161,150,155,230,221,226,216,205,212,87,97,90,81,76,280,355,341,360,350,366,374,345,375,330,335,142,147,292,137,127,132,24,10,16,266,25,30,311,309,310,308,306,307,6,5,277,63,68,73,52,57,272,37,42,47,261,251,256,245,236,241,175,180,187,192,197,202,287,102,107,112,117,122,295,166,171,160,151,156,232,220,227,215,206,210,86,95,92,82,77,282,357,342,362,352,365,370,347,376,331,336,140,145,291,135,125,130,23,14,19,269,29,34,314,312,313,317,315,316,4,1,276,60,65,71,51,56,270,35,40,45,264,254,259,249,239,244,179,184,189,194,199,204,286,101,106,111,115,120,299,169,174,164,154,159,234,224,229,219,209,214,85,96,91,80,75,281,356,340,361,351,369,373,346,379,334,339 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, M = {67} 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 23:45:17 · history