Equation 677 Database

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Magma d4ac5553f19d…

magma d4ac5553f19d
Size
381
Isomorphism class hash
d4ac5553f19d114aff5514b4b9d4933bac6387e4586640e6f55d3912c4de6469
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 23:48:02
Display reorder
380,297,37,36,38,35,34,212,33,272,32,30,31,306,307,308,309,310,311,140,146,135,126,131,121,185,190,180,201,206,196,261,265,275,247,252,256,232,237,287,217,222,227,39,40,41,42,242,43,111,290,116,95,100,105,171,166,176,150,156,161,91,280,86,75,80,70,340,347,361,352,366,357,337,331,376,374,298,51,52,48,49,50,213,46,274,45,44,47,313,314,312,316,317,315,142,147,137,127,132,120,187,192,182,202,207,197,263,268,278,249,254,258,233,238,288,218,223,228,55,57,56,53,243,54,110,291,115,97,101,106,172,167,177,152,157,162,92,282,87,77,82,73,342,348,362,351,367,358,338,332,377,370,295,20,19,17,18,16,211,15,270,14,12,13,325,326,324,328,329,327,144,149,139,129,134,124,189,194,184,204,209,199,262,267,277,248,253,257,231,236,286,215,220,225,28,29,27,5,241,4,114,294,119,99,104,109,174,169,179,154,159,164,94,284,89,79,81,71,344,346,364,354,369,355,336,334,379,373,296,21,8,11,9,10,210,1,271,0,2,3,302,301,300,305,303,304,141,145,136,125,130,122,186,191,181,200,205,195,260,266,276,246,251,255,230,235,285,216,221,226,23,24,22,26,240,25,112,292,117,96,102,107,170,165,175,151,155,160,90,281,85,76,84,72,341,345,360,350,365,356,335,330,375,371,299,66,65,63,64,62,214,61,273,60,58,59,320,318,319,323,321,322,143,148,138,128,133,123,188,193,183,203,208,198,264,269,279,245,250,259,234,239,289,219,224,229,7,69,6,68,244,67,113,293,118,98,103,108,173,168,178,153,158,163,93,283,88,78,83,74,343,349,363,353,368,359,339,333,378,372 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#e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76, M = {70} 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 23:48:03 · history