Equation 677 Database

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Magma a087cbe8a80e…

magma a087cbe8a80e
Size
381
Isomorphism class hash
a087cbe8a80eddac6f0917bb4dbe358c654275bde2b17a3ffadc2eabaf56661c
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 23:24:21
Display reorder
380,88,84,79,99,104,94,329,327,328,326,324,325,274,278,284,289,294,299,72,73,209,70,74,71,114,119,109,129,134,124,61,62,60,199,64,63,259,264,269,244,249,254,239,229,234,224,214,219,144,149,139,159,164,154,67,204,68,66,69,65,184,189,174,194,169,179,354,344,379,349,339,364,334,359,374,369,86,81,76,97,102,92,313,314,312,316,317,315,270,276,281,285,290,295,2,3,206,1,14,0,112,117,107,127,132,122,30,31,29,197,33,32,255,260,266,240,245,250,235,226,231,221,210,215,142,147,137,157,162,152,37,202,38,36,34,35,182,187,172,192,167,177,351,342,377,346,337,360,332,357,372,365,85,82,77,96,100,91,301,300,302,303,304,305,272,277,282,287,292,297,17,18,207,15,16,19,111,116,106,125,131,120,46,44,45,195,47,48,256,261,265,241,246,251,236,225,230,220,211,216,140,145,135,156,160,151,25,201,54,26,27,28,180,185,171,191,166,176,350,341,376,347,335,361,331,355,370,367,87,83,78,98,103,93,306,307,308,309,310,311,273,279,283,288,293,298,8,7,208,6,4,5,113,118,108,128,133,123,57,55,56,198,58,59,258,263,268,243,248,253,238,228,233,223,213,218,143,148,138,158,163,153,42,203,43,41,39,40,183,188,173,193,168,178,353,343,378,348,338,363,333,358,373,368,89,80,75,95,101,90,321,322,323,318,319,320,271,275,280,286,291,296,12,13,205,9,10,11,110,115,105,126,130,121,22,23,24,196,20,21,257,262,267,242,247,252,237,227,232,222,212,217,141,146,136,155,161,150,52,200,53,51,49,50,181,186,170,190,165,175,352,340,375,345,336,362,330,356,371,366 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#4b20d49131fa1763d6463a102f127bf88ae35086a2437318b417535ceb91dad1, M = {71} 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 23:24:22 · history