Equation 677 Database

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Magma cb04a1ca9630…

magma cb04a1ca9630
Size
381
Isomorphism class hash
cb04a1ca96305dfa11310107db225b9a6d2ea8513f72155b139cc72d9293d98b
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 23:33:36
Display reorder
380,110,109,111,112,113,108,202,212,222,232,181,191,84,85,86,87,88,89,248,259,269,279,289,299,99,100,101,96,97,98,91,92,93,94,95,90,252,262,272,282,290,241,103,104,105,106,107,102,118,119,114,115,116,117,199,209,219,229,239,189,317,316,312,313,314,315,347,349,368,350,348,372,332,346,364,379,146,145,147,148,149,144,200,210,220,230,188,198,57,58,59,54,55,56,243,254,264,274,284,294,71,66,67,68,69,70,51,52,53,48,49,50,250,260,270,280,292,240,62,63,64,65,60,61,154,155,150,151,152,153,193,204,214,224,234,183,323,322,318,319,320,321,341,343,366,356,344,371,355,342,369,374,22,21,23,18,19,20,205,215,225,235,184,194,141,142,143,138,139,140,249,251,261,271,281,291,76,77,72,73,74,75,135,136,137,132,133,134,255,265,275,285,295,244,81,82,83,78,79,80,16,17,12,13,14,15,190,201,211,221,231,180,328,327,329,324,325,326,353,345,361,336,333,375,337,354,362,370,1,5,0,2,3,4,208,218,228,238,186,196,179,174,175,176,177,178,242,253,263,273,283,293,156,157,158,159,160,161,168,169,170,171,172,173,258,268,278,288,298,247,167,162,163,164,165,166,9,10,11,6,7,8,192,203,213,223,233,182,310,309,311,306,307,308,331,358,360,335,357,378,334,359,365,373,129,128,130,131,126,127,206,216,226,236,187,197,37,38,39,40,41,36,246,257,267,277,287,297,28,29,24,25,26,27,45,46,47,42,43,44,256,266,276,286,296,245,33,34,35,30,31,32,125,120,121,122,123,124,195,207,217,227,237,185,301,305,300,302,303,304,340,338,367,351,330,376,352,339,363,377 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, 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 23:33:37 · history