Equation 677 Database

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Magma 6ec96a22e41e…

magma 6ec96a22e41e
Size
381
Isomorphism class hash
6ec96a22e41e5897e609c4c473d7882d9e4187e11df897ac340664ca74df42cc
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 23:39:06
Display reorder
380,77,39,38,41,42,40,292,207,212,202,192,197,51,52,50,54,250,53,177,182,187,162,167,172,44,45,46,47,48,255,107,112,116,121,126,131,240,246,235,226,231,221,270,260,265,296,276,281,314,312,313,317,315,316,145,150,156,136,285,141,78,80,79,217,81,82,345,340,335,357,331,351,362,366,373,377,83,19,18,16,17,15,293,208,213,203,193,198,57,58,59,55,252,56,178,183,188,163,168,173,31,32,30,28,29,257,108,114,117,122,127,132,242,247,237,227,232,222,272,264,269,297,277,282,321,322,323,318,319,320,148,153,158,138,288,143,84,86,85,218,87,88,347,342,337,359,332,353,363,368,372,378,70,23,24,20,21,22,290,205,210,201,191,196,61,62,60,64,253,63,175,180,185,161,166,171,65,69,66,67,68,258,109,111,119,123,128,133,243,248,238,228,233,223,273,263,268,298,278,283,300,302,301,304,305,303,147,152,157,137,287,142,71,73,72,215,74,75,348,343,338,355,333,352,360,367,370,376,6,5,7,8,9,10,291,206,211,200,190,195,37,35,36,34,251,33,176,181,186,160,165,170,3,49,4,0,2,256,106,113,115,120,125,130,241,245,236,225,230,220,271,262,267,295,275,280,309,310,311,306,307,308,146,151,155,135,286,140,76,14,13,216,12,11,346,341,336,356,330,350,361,365,371,375,99,43,1,26,27,25,294,209,214,204,194,199,90,91,89,93,254,92,179,184,189,164,169,174,94,98,95,96,97,259,105,110,118,124,129,134,244,249,239,229,234,224,274,261,266,299,279,284,325,326,324,328,329,327,149,154,159,139,289,144,100,102,101,219,103,104,349,344,339,358,334,354,364,369,374,379 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 = {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 23:39:07 · history