Equation 677 Database

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Magma 6c8e681ad2ad…

magma 6c8e681ad2ad
Size
381
Isomorphism class hash
6c8e681ad2ad3b6b7f0282b38884e9c76364fe4af77097c51c4fc93aa8156302
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 23:38:54
Display reorder
380,184,177,189,194,199,204,129,133,139,142,292,147,114,104,109,289,119,124,59,64,54,279,74,69,251,256,261,235,240,245,297,172,167,159,164,152,10,2,6,269,15,24,229,234,224,214,219,209,274,29,34,39,44,49,308,306,307,311,309,310,99,284,94,84,89,79,374,334,359,362,339,353,367,344,349,377,183,176,187,193,197,203,125,131,136,141,290,146,111,101,106,285,115,120,56,61,51,275,71,66,250,255,260,237,242,247,295,170,166,158,163,150,13,3,7,266,16,21,226,231,221,211,215,206,270,26,31,36,40,45,320,318,319,329,321,322,95,281,90,81,86,75,371,330,355,360,335,351,365,340,345,375,180,178,186,191,196,201,127,130,137,143,293,148,112,102,107,286,117,122,57,62,50,276,70,65,252,257,262,236,241,246,298,173,168,156,161,153,12,0,8,265,19,20,227,232,222,212,217,207,271,25,30,35,41,46,314,312,313,317,315,316,96,280,91,80,85,76,372,332,356,363,336,350,368,341,346,378,181,179,185,190,195,200,126,134,135,144,294,149,113,103,108,288,118,123,58,63,53,278,73,68,254,259,264,239,244,249,299,174,169,155,160,154,14,4,9,268,18,23,228,233,223,213,218,208,273,28,33,38,43,48,300,302,301,304,305,303,98,283,93,83,88,78,373,333,358,364,338,352,369,343,348,379,182,175,188,192,198,202,128,132,138,140,291,145,110,100,105,287,116,121,55,60,52,277,72,67,253,258,263,238,243,248,296,171,165,157,162,151,11,1,5,267,17,22,225,230,220,210,216,205,272,27,32,37,42,47,328,326,327,325,323,324,97,282,92,82,87,77,370,331,357,361,337,354,366,342,347,376 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#a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f, 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 23:38:54 · history