Equation 677 Database

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Magma e541e586f8b2…

magma e541e586f8b2
Size
381
Isomorphism class hash
e541e586f8b2c61d52067c0901f28f082d96fabe47270979d00e054b373d866c
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 23:43:45
Display reorder
380,71,62,76,63,85,81,80,72,307,67,69,60,77,64,86,68,82,78,73,305,70,61,75,65,84,66,83,79,74,306,106,92,93,115,97,111,110,102,310,101,99,90,107,94,116,98,112,108,103,308,100,91,105,95,114,96,113,109,104,309,118,119,87,88,89,117,365,351,366,376,370,338,379,367,352,337,144,135,121,139,130,126,125,148,300,143,145,136,122,140,131,141,127,123,149,301,146,137,120,138,129,142,128,124,147,321,151,165,169,160,173,156,155,178,303,174,175,166,152,170,161,171,157,153,179,304,176,167,150,168,159,172,158,154,177,302,163,164,132,133,134,162,373,364,363,345,358,344,372,359,360,343,192,183,200,187,235,229,201,196,312,191,193,184,198,188,236,189,230,202,197,313,194,185,199,186,234,190,228,203,195,311,224,207,211,238,215,232,225,220,315,216,217,208,222,212,239,213,233,226,221,316,218,209,223,210,237,214,231,227,219,314,205,206,180,181,182,204,371,355,341,330,332,331,353,354,342,356,290,272,241,277,259,257,248,295,327,282,288,270,240,278,260,283,254,247,296,326,289,271,242,276,258,284,255,246,294,322,245,273,280,262,287,256,249,298,325,291,292,274,243,281,263,285,252,250,299,323,293,275,244,279,261,286,253,251,297,324,268,269,265,266,264,267,347,357,333,349,369,374,377,346,339,348,53,44,58,45,36,35,31,54,320,49,51,42,59,46,37,50,33,32,55,329,52,43,57,47,38,48,34,30,56,319,28,14,15,6,19,5,0,24,317,23,21,12,29,16,7,20,3,2,25,318,22,13,27,17,8,18,4,1,26,328,9,10,41,39,40,11,375,350,334,378,336,368,362,335,361,340 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#ccdb12afb22da8ed9220f5a50b1f559a5f1d11488934a41ba79194e674f7c3c3, 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 23:43:46 · history