Equation 677 Database

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Magma fac299e09a7b…

magma fac299e09a7b
Size
381
Isomorphism class hash
fac299e09a7b03cf5c387a98a11761e98e820bf368f654271fb5f404cc37594d
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 23:18:28
Display reorder
380,158,153,148,138,143,133,118,123,128,103,108,113,268,273,278,254,259,263,73,63,68,58,293,53,198,203,193,213,218,208,83,88,78,98,298,93,28,288,34,38,43,48,238,243,248,224,229,233,282,22,17,7,13,3,306,307,308,309,310,311,173,163,168,188,178,183,362,333,338,348,343,353,358,378,368,373,155,151,146,136,141,130,115,120,126,101,106,111,267,272,277,253,258,262,71,61,66,55,290,51,196,201,190,210,215,205,81,86,75,95,296,90,26,285,32,35,40,46,237,242,246,221,227,231,281,20,15,6,12,1,323,321,322,320,318,319,171,161,166,186,176,181,364,330,335,345,340,351,355,375,365,371,159,154,149,139,144,134,119,124,129,104,109,114,269,274,279,250,255,264,74,64,69,59,294,54,199,204,194,214,219,209,84,89,79,99,299,94,29,289,31,39,44,49,239,244,249,220,225,234,284,24,18,9,14,4,328,329,327,325,326,324,174,164,169,189,179,184,363,334,339,349,344,354,359,379,369,374,156,150,145,137,140,132,117,122,127,102,107,112,265,270,276,252,257,261,70,60,65,56,291,50,197,202,192,212,217,207,82,87,77,97,297,92,25,286,30,36,41,45,235,240,245,223,228,232,280,21,16,5,11,2,316,317,315,313,314,312,170,162,165,185,175,180,361,332,336,346,341,352,357,377,367,372,157,152,147,135,142,131,116,121,125,100,105,110,266,271,275,251,256,260,72,62,67,57,292,52,195,200,191,211,216,206,80,85,76,96,295,91,27,287,33,37,42,47,236,241,247,222,226,230,283,23,19,8,10,0,303,304,305,301,300,302,172,160,167,187,177,182,360,331,337,347,342,350,356,376,366,370 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, 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 23:18:28 · history