Equation 677 Database

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Magma 558c72f01a9a…

magma 558c72f01a9a
Size
381
Isomorphism class hash
558c72f01a9a37cacbdacb0448923e2cc39a070ed5e2a92819be20c6073bd408
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 23:23:14
Display reorder
380,286,115,120,100,106,111,183,188,177,198,203,193,208,213,218,223,228,233,319,320,318,322,323,321,270,26,31,35,40,46,281,95,90,80,86,75,264,254,259,249,238,243,168,298,173,152,158,163,265,19,20,14,4,8,65,70,276,50,55,61,125,291,130,136,141,147,356,367,340,332,372,346,361,336,351,377,287,118,122,103,108,113,182,186,176,196,202,192,205,210,215,221,226,230,311,309,310,308,306,307,273,28,33,38,43,48,283,98,93,83,88,78,260,251,256,246,235,240,166,296,170,151,156,160,268,17,23,11,0,5,68,73,278,53,58,63,126,290,131,135,142,145,357,366,343,331,371,348,360,338,353,376,289,119,124,104,109,114,181,187,175,197,201,191,206,211,216,220,225,231,305,303,304,302,301,300,274,29,34,39,44,49,284,99,94,84,89,79,262,252,257,248,237,242,165,295,171,150,155,161,269,18,24,12,2,7,69,74,279,54,59,64,129,294,134,139,140,146,359,365,344,334,370,349,364,339,354,375,288,117,123,102,107,112,180,185,179,195,200,190,209,214,219,224,229,234,317,315,316,314,312,313,271,25,30,36,41,45,282,97,92,82,87,77,263,253,258,245,239,244,167,297,172,154,157,162,266,16,21,13,3,9,66,71,275,51,56,60,128,293,133,138,144,149,358,369,341,333,373,345,363,335,352,379,285,116,121,101,105,110,184,189,178,199,204,194,207,212,217,222,227,232,325,326,324,328,329,327,272,27,32,37,42,47,280,96,91,81,85,76,261,250,255,247,236,241,169,299,174,153,159,164,267,15,22,10,1,6,67,72,277,52,57,62,127,292,132,137,143,148,355,368,342,330,374,347,362,337,350,378 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 = {74} 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 23:23:15 · history