Equation 677 Database

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Magma 5c113e95d42e…

magma 5c113e95d42e
Size
381
Isomorphism class hash
5c113e95d42e82ff35201310b99f3c07e7198ff990650681efbe8910ab96b57f
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 23:30:10
Display reorder
380,37,46,32,50,42,33,327,59,55,41,47,38,30,48,43,34,39,328,57,56,40,36,45,31,49,44,35,326,58,54,11,29,20,3,16,7,12,324,2,21,22,27,9,18,4,17,8,13,325,1,23,28,10,19,5,15,6,14,323,0,24,25,52,53,51,26,338,376,339,375,333,349,350,348,347,362,261,279,251,286,275,253,311,244,297,268,280,262,249,287,273,257,269,312,245,298,267,263,281,250,285,274,252,313,243,299,259,295,277,247,272,256,264,314,242,282,283,296,260,278,246,270,254,265,315,241,284,294,258,276,248,271,255,266,316,240,289,290,291,292,293,288,358,345,332,369,357,360,331,359,346,361,148,126,143,130,125,144,309,139,135,121,127,149,141,131,123,145,122,310,140,136,120,147,128,142,129,124,146,308,138,137,174,164,155,169,151,173,178,307,165,156,157,162,175,153,170,152,171,179,329,166,158,163,176,154,168,150,172,177,306,167,159,160,132,133,134,161,372,365,363,364,377,370,351,335,334,352,92,101,115,102,97,119,304,111,110,93,99,90,116,103,98,117,94,305,112,108,95,91,100,114,104,96,118,303,113,109,63,81,72,89,71,62,67,300,85,76,77,82,64,73,87,69,60,68,302,86,75,83,65,74,88,70,61,66,301,84,79,80,107,105,106,78,379,336,337,378,374,373,354,353,366,367,231,198,220,202,197,227,317,213,207,238,199,232,221,203,195,225,239,318,211,208,237,233,200,219,201,196,226,319,212,209,228,193,184,218,180,223,236,320,214,188,186,194,229,185,216,181,224,234,321,210,187,192,230,183,217,182,222,235,322,215,191,189,204,205,206,190,330,343,371,356,344,368,355,340,341,342 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#609c8488c1221ec7cc1b224882281cdf16c044d84dccec5c4b9550762e96f98c, M = {66} 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 23:30:11 · history