Equation 677 Database

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Magma 51310823c735…

magma 51310823c735
Size
381
Isomorphism class hash
51310823c73519739834f4c48478bdbdd08f1d0dd488c1751dc25a41b486e65e
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 23:38:30
Display reorder
380,213,208,218,223,228,233,93,98,88,78,82,73,47,48,49,50,51,198,43,44,42,46,193,45,163,168,173,178,183,188,288,298,284,273,278,268,293,55,203,54,52,53,315,316,317,312,313,314,238,243,248,253,258,263,143,133,138,158,148,153,108,103,113,118,123,128,333,343,363,348,354,373,358,378,338,368,210,205,215,221,226,230,91,96,86,76,81,71,18,19,20,21,22,195,7,8,9,5,191,6,160,165,171,175,180,185,286,296,282,270,275,266,290,10,201,11,27,12,323,321,322,320,318,319,236,241,245,251,256,260,140,130,135,156,146,151,105,100,110,116,121,126,330,340,361,346,351,371,355,375,336,365,214,209,219,224,229,234,94,99,89,79,83,74,61,62,63,64,65,199,57,58,56,60,194,59,164,169,174,179,184,189,289,299,281,274,279,269,294,69,204,68,66,67,326,324,325,329,327,328,239,244,249,254,259,264,144,134,139,159,149,154,109,104,114,119,124,129,334,344,364,349,353,374,359,379,339,369,212,207,217,222,227,232,92,97,87,77,84,72,33,34,35,36,37,197,29,30,28,32,192,31,162,167,172,177,182,187,287,297,283,272,277,267,292,41,202,40,38,39,310,311,309,307,308,306,237,242,247,252,257,262,142,132,137,157,147,152,107,102,112,117,122,127,332,342,362,347,352,372,357,377,337,367,211,206,216,220,225,231,90,95,85,75,80,70,3,4,2,1,0,196,14,15,13,17,190,16,161,166,170,176,181,186,285,295,280,271,276,265,291,26,200,25,23,24,303,304,305,301,300,302,235,240,246,250,255,261,141,131,136,155,145,150,106,101,111,115,120,125,331,341,360,345,350,370,356,376,335,366 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 = {66} 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 23:38:31 · history