Equation 677 Database

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Magma b99fc9f09d42…

magma b99fc9f09d42
Size
381
Isomorphism class hash
b99fc9f09d420219a4acea646fe2fd8a2f4054ed6d713c3958b33139ee16f34b
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 23:30:06
Display reorder
380,304,303,305,301,300,302,123,128,118,108,113,100,148,153,158,133,138,143,221,36,37,44,34,35,53,52,59,51,50,231,170,160,165,185,176,181,89,77,81,95,90,296,192,197,202,207,212,217,255,260,251,242,247,237,267,278,271,290,280,285,47,227,48,46,49,45,347,375,351,330,361,336,342,356,367,371,310,309,311,306,307,308,120,126,115,106,111,102,146,151,155,131,136,140,223,63,64,62,60,61,16,14,15,18,17,232,172,162,167,187,177,182,86,78,82,97,92,297,191,195,200,206,210,215,258,263,253,243,248,238,266,276,274,293,282,288,20,229,19,22,23,21,348,377,352,331,362,338,344,357,368,372,327,329,328,326,324,325,124,129,119,109,114,101,149,154,159,134,139,144,224,68,69,67,65,66,4,5,38,12,13,230,171,161,166,186,175,180,85,75,80,98,93,298,190,196,201,205,211,216,257,262,252,240,245,236,268,277,272,291,281,286,3,226,2,1,0,11,345,376,350,333,360,339,341,355,365,370,314,313,312,316,317,315,121,125,116,105,110,104,145,150,156,130,135,141,222,57,58,56,54,55,28,26,27,25,24,233,174,164,169,189,179,184,87,76,84,96,91,295,194,199,204,209,214,219,256,261,250,241,246,235,265,275,270,292,284,287,30,228,29,32,33,31,346,379,354,334,364,337,343,359,366,374,318,320,319,323,321,322,122,127,117,107,112,103,147,152,157,132,137,142,220,42,43,41,39,40,74,70,71,72,73,234,173,163,168,188,178,183,88,79,83,99,94,299,193,198,203,208,213,218,259,264,254,244,249,239,269,279,273,294,283,289,9,225,10,8,6,7,349,378,353,332,363,335,340,358,369,373 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#6034e0b6e760ca1a616002bdffba2c9ecdf9d8efbd60a04eea2e11213baf5719, M = {75} 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 23:30:07 · history