Equation 677 Database

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Magma 2467210c52c0…

magma 2467210c52c0
Size
381
Isomorphism class hash
2467210c52c012c2e5a613f55523afd49694d77effe04833120cc0b2670ab8be
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 23:38:02
Display reorder
380,67,217,68,66,64,65,238,228,233,298,243,248,256,260,265,271,279,286,13,11,12,250,14,15,168,173,178,153,158,163,197,202,207,182,187,192,323,324,325,326,327,328,143,148,138,128,133,123,107,113,118,293,98,103,69,70,283,223,48,71,0,1,63,61,62,212,337,348,363,332,368,373,375,342,352,358,92,219,93,91,89,90,239,229,234,299,244,249,259,264,269,272,275,287,19,20,18,252,17,16,169,174,179,154,159,164,199,204,209,184,189,194,311,309,310,308,306,307,144,149,139,129,134,124,108,114,119,294,99,104,82,85,284,224,83,84,87,86,88,6,94,214,339,349,364,334,369,374,379,344,353,359,33,216,32,30,31,60,235,226,231,295,240,245,258,262,267,273,276,289,8,47,7,251,9,10,166,171,176,150,155,160,195,201,206,181,186,191,312,313,314,315,316,329,141,146,136,125,130,121,105,111,115,292,95,100,35,34,281,220,36,37,50,49,51,52,53,210,335,345,361,331,366,370,378,341,351,355,58,215,59,57,55,56,236,225,230,296,241,246,255,261,266,270,278,285,27,25,26,253,28,29,167,172,177,152,157,162,196,200,205,180,185,190,303,304,305,301,300,302,142,147,137,127,132,122,109,112,117,290,97,102,23,24,280,221,21,22,2,3,54,5,4,211,336,346,362,330,367,372,376,340,350,356,79,218,80,78,81,77,237,227,232,297,242,247,257,263,268,274,277,288,44,42,43,254,45,46,165,170,175,151,156,161,198,203,208,183,188,193,318,319,317,321,322,320,140,145,135,126,131,120,106,110,116,291,96,101,39,40,282,222,38,41,73,72,74,75,76,213,338,347,360,333,365,371,377,343,354,357 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#9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f, 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 23:38:03 · history