Equation 677 Database

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Magma 9f8496fe0e42…

magma 9f8496fe0e42
Size
381
Isomorphism class hash
9f8496fe0e42c558a99e29c70b9b50dfac3085483c998b702aed344374acca0c
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 23:16:46
Display reorder
380,132,137,133,134,135,136,241,246,251,256,261,265,129,130,131,126,127,128,155,161,166,171,176,150,121,122,123,124,125,120,200,205,181,185,190,195,302,303,304,305,301,300,143,138,139,140,141,142,286,290,295,271,276,281,146,147,148,149,144,145,211,235,215,220,225,230,335,361,352,343,369,371,359,338,349,377,100,99,101,96,97,98,243,248,253,258,263,268,90,91,92,93,94,95,158,163,168,173,178,153,117,118,119,114,115,116,203,208,183,188,193,198,316,317,312,313,314,315,103,104,105,106,107,102,288,293,298,273,278,283,112,113,108,109,110,111,213,238,218,223,228,233,348,362,353,347,366,372,355,337,341,378,32,31,33,34,35,30,242,247,252,257,262,267,54,55,56,57,58,59,157,162,167,172,177,152,53,48,49,50,51,52,202,207,182,187,192,197,327,328,329,324,325,326,38,39,40,41,36,37,287,292,297,272,277,282,47,42,43,44,45,46,212,237,217,222,227,232,334,364,354,346,367,370,357,340,345,375,85,84,86,87,88,89,240,245,250,255,260,266,80,81,82,83,78,79,156,160,165,170,175,151,75,76,77,72,73,74,201,206,180,186,191,196,306,307,308,309,310,311,61,62,63,64,65,60,285,291,296,270,275,280,70,71,66,67,68,69,210,236,216,221,226,231,331,360,351,330,368,374,358,344,342,376,19,18,20,21,22,23,244,249,254,259,264,269,14,15,16,17,12,13,159,164,169,174,179,154,9,10,11,6,7,8,204,209,184,189,194,199,321,322,323,318,319,320,27,28,29,24,25,26,289,294,299,274,279,284,4,5,1,0,2,3,214,239,219,224,229,234,336,363,350,339,365,373,356,333,332,379 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#09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1, M = {68} 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 23:16:47 · history