Equation 677 Database

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Magma c77918b81cb6…

magma c77918b81cb6
Size
381
Isomorphism class hash
c77918b81cb67397332cb453ff8f03f565c4f9e41cb5bf5e9efe452cf16f7b27
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 23:38:46
Display reorder
380,125,124,130,136,141,145,321,322,323,318,319,320,154,159,164,169,174,179,74,20,19,218,72,73,264,269,259,279,289,274,78,79,77,254,81,80,21,22,223,75,76,283,199,204,209,184,189,194,294,119,114,104,105,99,243,248,298,228,233,238,67,71,68,213,69,70,334,369,364,348,357,338,379,354,343,374,127,122,132,137,142,147,317,315,316,314,312,313,152,157,162,167,172,177,3,39,2,216,4,5,263,268,258,278,288,273,17,18,66,253,64,65,40,41,220,1,0,281,197,202,207,182,187,192,293,117,112,103,107,98,241,245,295,227,232,237,28,30,29,210,31,32,332,368,362,345,356,335,378,352,341,372,126,121,131,135,140,146,311,309,310,308,306,307,151,156,161,165,170,175,36,34,35,215,37,38,262,267,257,275,285,270,50,51,49,252,53,52,8,7,221,42,43,280,196,201,206,180,185,190,291,115,110,100,109,97,242,247,297,225,230,235,33,16,15,211,14,13,331,367,360,346,355,336,377,351,340,370,128,123,133,138,143,148,324,325,326,327,328,329,153,158,163,168,173,178,88,91,87,219,89,90,260,265,256,277,286,272,46,44,45,250,47,48,92,93,224,6,94,284,198,203,208,183,188,193,292,118,113,101,108,96,244,249,299,229,234,239,82,84,83,214,85,86,333,365,363,349,358,339,375,353,344,373,129,120,134,139,144,149,305,303,304,302,301,300,150,155,160,166,171,176,61,11,12,217,59,60,261,266,255,276,287,271,24,25,23,251,27,26,9,10,222,62,63,282,195,200,205,181,186,191,290,116,111,102,106,95,240,246,296,226,231,236,54,58,55,212,56,57,330,366,361,347,359,337,376,350,342,371 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 = {69} 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 23:38:46 · history