Equation 677 Database

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Magma 612b915a08db…

magma 612b915a08db
Size
381
Isomorphism class hash
612b915a08db379a903d9733fe2200c9e6bdb4328c923cc3ad3837a137a09710
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 23:26:32
Display reorder
380,313,312,314,315,316,317,175,151,156,161,166,171,265,241,246,251,255,260,28,29,24,25,26,27,16,17,12,13,14,15,21,22,23,18,19,20,290,295,271,276,281,285,3,4,5,1,0,2,221,226,231,235,211,216,9,10,11,6,7,8,196,191,201,205,181,186,335,376,356,333,346,369,349,360,371,338,301,305,300,302,303,304,177,152,157,162,167,172,267,242,247,252,257,262,103,104,106,108,110,112,132,134,136,127,129,131,143,144,146,148,139,141,292,297,272,277,282,287,124,115,117,119,121,122,222,227,232,237,212,217,98,100,91,93,94,96,197,192,202,207,182,187,342,377,357,343,353,365,350,363,373,334,323,322,318,319,320,321,179,154,159,164,169,174,269,244,249,254,259,264,88,89,84,85,86,87,76,77,72,73,74,75,81,82,83,78,79,80,294,299,274,279,284,289,63,64,65,60,61,62,224,229,234,239,214,219,69,70,71,66,67,68,199,194,204,209,184,189,339,378,355,332,345,368,352,361,374,340,307,306,308,309,310,311,178,153,158,163,168,173,268,243,248,253,258,263,102,105,107,109,111,113,133,135,137,126,128,130,142,145,147,149,138,140,293,298,273,278,283,288,125,114,116,118,120,123,223,228,233,238,213,218,99,101,90,92,95,97,198,193,203,208,183,188,341,379,358,344,354,367,351,364,370,331,327,326,328,329,324,325,176,150,155,160,165,170,266,240,245,250,256,261,58,59,54,55,56,57,46,47,42,43,44,45,51,52,53,48,49,50,291,296,270,275,280,286,33,34,35,30,31,32,220,225,230,236,210,215,39,40,41,36,37,38,195,190,200,206,180,185,336,375,359,330,347,366,348,362,372,337 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, M = {67} 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 23:26:33 · history