Equation 677 Database

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Magma eaeabd651b39…

magma eaeabd651b39
Size
381
Isomorphism class hash
eaeabd651b3917088f2ff296de86a8565b8fa8b18d07ab98f2427b928c7239a1
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 23:44:33
Display reorder
380,191,181,200,210,220,230,26,27,28,29,24,25,115,116,117,118,119,114,31,32,33,34,35,30,253,263,273,283,293,243,306,307,308,309,310,311,223,233,183,193,203,213,110,111,112,113,108,109,102,103,104,105,106,107,281,271,98,99,100,290,241,101,251,96,261,97,347,348,346,373,370,336,349,363,360,335,192,182,202,212,222,232,20,21,22,23,18,19,168,169,170,171,172,173,16,17,12,13,14,15,254,264,274,284,294,244,321,322,323,318,319,320,224,234,184,194,204,214,178,179,174,175,176,177,78,79,80,81,82,83,282,272,74,75,76,292,242,77,252,72,262,73,343,359,342,374,372,330,358,369,362,334,197,187,207,217,227,237,64,65,60,61,62,63,159,160,161,156,157,158,66,67,68,69,70,71,256,266,276,286,296,246,300,302,303,304,305,301,226,236,186,196,206,216,162,163,164,165,166,167,152,153,154,155,150,151,287,277,145,146,147,297,247,148,257,149,267,144,355,357,354,376,377,341,356,365,368,331,195,185,205,215,225,235,121,122,123,124,125,120,55,56,57,58,59,54,128,129,130,131,126,127,258,268,278,288,298,248,315,316,317,312,313,314,228,238,188,198,208,218,50,51,52,53,48,49,44,45,46,47,42,43,285,275,37,38,39,295,245,40,255,41,265,36,338,339,337,378,375,350,340,366,364,351,199,189,209,219,229,239,11,6,7,8,9,10,136,137,132,133,134,135,3,4,5,1,0,2,250,260,270,280,291,240,327,328,329,324,325,326,221,231,180,190,201,211,140,141,142,143,138,139,92,93,94,95,90,91,289,279,85,86,87,299,249,88,259,89,269,84,345,352,344,371,379,332,353,361,367,333 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#d9df7de9a291eb9f8afa3ed926081c844b8ee7df4e18920313d7d7d6494810a4, 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 23:44:34 · history