Equation 677 Database

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Magma 011aa7d22427…

magma 011aa7d22427
Size
381
Isomorphism class hash
011aa7d22427e9290e4a8a212f6a434e63df1a444dcce411686115699cdbb584
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 23:16:41
Display reorder
380,146,141,151,155,160,136,21,22,23,24,25,20,281,291,53,12,13,271,17,18,19,14,15,16,5,1,0,2,3,4,266,240,245,251,256,261,196,276,286,295,200,205,220,225,230,236,210,215,185,190,166,171,176,181,10,11,6,7,8,9,326,325,327,328,329,324,335,333,332,379,356,336,360,369,371,350,149,144,153,158,163,138,115,116,117,118,119,114,280,294,132,133,134,274,111,112,113,108,109,110,124,125,120,121,122,123,268,244,249,254,259,263,199,279,288,298,204,209,223,229,234,239,214,219,188,193,168,174,179,183,129,130,131,126,127,128,312,317,313,314,315,316,340,334,348,377,359,349,362,367,372,352,147,142,152,157,162,137,29,30,31,26,27,28,282,290,50,51,52,270,33,34,35,36,37,32,40,41,42,43,38,39,267,242,247,252,257,262,197,277,287,297,202,207,222,227,232,237,212,217,187,192,167,172,177,182,45,46,47,48,49,44,308,307,309,310,311,306,338,341,339,378,357,337,361,368,370,354,148,143,154,159,164,139,62,57,58,59,60,61,283,292,54,55,56,272,76,77,78,79,80,75,64,65,66,67,68,63,269,243,248,253,258,264,198,278,289,299,203,208,224,228,233,238,213,218,189,194,169,173,178,184,69,70,71,72,73,74,302,300,303,304,305,301,344,330,343,376,358,342,363,366,373,353,145,140,150,156,161,135,103,104,99,100,101,102,284,293,105,106,107,273,94,95,96,97,98,93,82,83,84,85,86,81,265,241,246,250,255,260,195,275,285,296,201,206,221,226,231,235,211,216,186,191,165,170,175,180,87,88,89,90,91,92,320,319,321,322,323,318,345,331,346,375,355,347,364,365,374,351 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#09de7e296fafc11e1910887718202808c6591641f036fb4e85591d955a2aaea1, M = {67} 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 23:16:43 · history