Equation 677 Database

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Magma 0f4718a53dcc…

magma 0f4718a53dcc
Size
381
Isomorphism class hash
0f4718a53dcc8f47192461e86a7e265aaf87f2d62b8a62fc2f24c4617dea81fc
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 23:26:10
Display reorder
380,6,11,7,8,9,10,288,294,299,274,279,284,18,19,20,21,22,23,12,13,14,15,16,17,305,301,300,302,303,304,34,35,30,31,32,33,189,194,199,204,209,184,214,219,224,229,234,239,27,28,29,24,25,26,244,249,254,259,264,269,164,174,154,169,179,159,339,337,353,362,366,338,378,374,330,357,124,123,115,117,119,121,286,292,297,270,275,281,100,91,92,94,96,98,129,131,133,135,136,127,308,309,310,311,306,307,148,139,141,143,145,147,185,190,195,200,205,181,210,215,220,225,231,236,106,108,110,112,103,104,240,245,251,256,261,266,162,172,152,167,177,157,349,347,354,355,368,344,376,372,335,363,48,53,49,50,51,52,285,291,296,272,277,282,59,54,55,56,57,58,2,3,4,5,1,0,314,315,316,317,312,313,42,43,44,45,46,47,186,191,196,201,206,180,211,216,221,226,230,235,37,38,39,40,41,36,241,246,250,255,260,265,161,171,150,166,176,156,336,332,350,360,365,340,379,371,343,358,125,122,114,116,118,120,287,293,298,273,278,283,101,90,93,95,97,99,128,130,132,134,137,126,328,329,324,325,326,327,149,138,140,142,144,146,188,193,198,203,208,183,213,218,223,228,233,238,107,109,111,113,102,105,243,248,253,258,263,268,163,173,153,168,178,158,348,346,352,361,369,345,377,373,331,364,85,84,86,87,88,89,289,290,295,271,276,280,70,71,66,67,68,69,73,74,75,76,77,72,318,319,320,321,322,323,83,78,79,80,81,82,187,192,197,202,207,182,212,217,222,227,232,237,65,60,61,62,63,64,242,247,252,257,262,267,160,170,151,165,175,155,334,341,351,356,367,342,375,370,333,359 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#50609e522fd5f79e53ac56beafcb5b424f2d261582798854b4ac2a2a84486b65, 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 23:26:11 · history